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Mechanical Drawing 


By 

De Witt Hunt, B. S. 

Head of Shop# Department . Oklahoma A. d M . College; 
Author of A Manual for Hand Woodworking; A Manual for 
Ma ch in e Woodworbing . 



HARLOW PUBLISHING COMPANY 
Oklahoma City, Oklahoma 
1926 




Copyright 1926 by 

HARLOW PUBLISHING COMPANY 



SEP 25 ’26 


©C1A950183 


'Y\ 0 [ 


PREFACE 

This text book has been planned on a dual outline. The 
first purpose has been to present drawing problems in a 
practical sequence, proceeding from the very easy to the 
easy, and from the easy, working very gradually, toward the 
difficult and the more difficult. The second purpose has been 
to present the informational material of mechanical drawing 
in a slowly developing regularity. These two aims are imper¬ 
fectly realized by listing the number of drawing problems like¬ 
ly to be completed in the public school drawing course, and 
grouping the instructional material or subject-matter around 
these problems. All models used as drawing problems have 
been selected because they suit the ability of the student 
at that time, and because the drawing of that particular 
model teaches the subject-matter under consideration in that 
stage of progression, in the series of drawing problems. 

In the assignments in this text, the student has several 
drawings to copy, several to complete by making the second- 
or third view, several to make from oblique projections and 
several to make from dimensioned photographs. Besides 
these, several written descriptions are given, together with 
a number of outside research assignments. In addition to 
these types of problems, the drawing teacher should pro¬ 
vide as many actual models, such as the IT. S. Machine Bolt, 
a Square Thread problem, several Packing Glands, a Globe 
I alve, etc., so that the student may secure experience in 
drawing from models. Projection screens similar to those 
in Chapter I should be provided as a part of the regular 
equipment of the drawing room. 

The order of assignment of drawing problems may and 
should be varied to suit local.needs as are discovered bv the 
drawing teachers. In some instances, problems covered in 
separate chapters may be included in a single drawing. Ink¬ 
ing may be delayed until after an entire semester or a full 
year has been spent in making pencil drawings. Lower case 


letters should not be presented until the student can easily 
master them, upper case letters being used exclusively prior 
to that time. Other variations from the progressions in this 
text should be made at the desire of the teacher. 


ACKNOWLEDGMENTS 

Much credit is due and an expression of appreciation is 
hereby made to The Eugene Deitzgen Company for furnish¬ 
ing the cuts for Figures 7, 8, 11, 12, 13, 18, 18a, 19, 21, 23, 
24, 25, 26, 27, 28, 30, 40, 43,45,46, 46a, 48, 59, 63, 68, 70, 73, 
74, 81, 107, 114, and 146. The effectiveness of this book 
would be greatly reduced without the use of these tine il¬ 
lustrations. An expression of appreciation is also made to 
The House and Garden Magazine for the use of Figure 75 
which was reproduced from their copy; to The American 
Builder Magazine for Figure 131 which was taken from 
their magazine; to The Southern Pine Associa'.ion for the 
privilege of making Plates NNH and XXIII from their 
book of garage plans; to The Briggs Lumber Company, pub¬ 
lishers of The Builder Magazine, from which the copy for 
Figure 133 was taken; to the Link-Belt Company for fur¬ 
nishing cuts for Figures 82 and 83; to the E. IT. Sheldon 
Company for the use of cuts for Figures 167 and 168; to 
Mr. L. Iv. Anderson who made the copy for Plate 1; and to 
The American Face Brick Association for furnishing cuts for 
Figures 130 and 132. 

Many of the line drawings in this Book were made by 
Mr. Henry G. Adams, who has been a student in my classes 
during the time this book has been in preparation, and an 
expression of appreciation to him is hereby made. 

De Witt Hunt 


CONTENTS 

Chapter Page 

I. The Theory of Mechanical Drawing - 1 

II. Pencils _ 9 

III. Lettering Practice _ 12 

IV. Drawing Paper. Erasing Pencil Lines. _ 17 

V. Laying Out the 9 x 12 Sheet - 19 

VI. Making Preliminary Sketches Before 

M AKING w or king Drawings_ _ 28 

VII. Making the Drawing - 32 

VIII. Invisible Lines_ 39 

IX. Representing Chamfers - 43 

X. Round Holes in or Through a Solid - 48 

XT. Inking the Letters on the Sheet - 53 

XII. Letter Sheet_ 56 

XIII. Cylinders - - - 59 

XIV. Dimensioning _ 6/ 

XV. Inking the Drawing. - 71 

XVI. Disc Forms _ 76 

XVII. Scale Drawing_ 80 

XVIII. Making Tracings_ '84 

XIX. Making Blue Prints - 88 

XX. The 10 x 14 Standard Sheet - 91 

XXL Sectional Views in Mechanical Draw- 


XXIT. Tangent Problems- 190 

XXIII. Tangent Problems, Case I-101 

XXIV. Tangent Problems, Case II-105 

XXV. Tangent Problems, Case Ill_108 

XXVI. Tangent Problems, Case TV-113 

XXVII. Tangent Problems, Case V-117 


























XXVIII. The Helix_121 

XXIX. “V” Threads_125 

XXX. Bolts and Nuts_131 

XXXI. Square Threads_135 

XX X11. Double-Triple-Multiple-Threaded 

Screws _:_138 

XXXIIT. Pipe Threads_140 

XXXIV. House Plans_ 142 

XXXV. Building Details_146 

XXX VI. Building Elevations_149 

XXXVII. Isometric Drawing_150 

XXXVIII. Oblique Projection_152 

XXXIX. Orthographic Projections of Lines and 

Points _153 

XL. Projections of Lines_156 

XII. True Length of Lines_158 

XLIT. Developments and Auxiliary Views_160 

XL11T. Pyramids and Cones__163 

XLIV. Conic Sections._ 167 

XLV. Intersections _ 170 

XLVI. Gymnastics of Mechanical Drawing_173 

XLVTI. Drawing Room Equipment_181 

XLVITI. Useful Tables._ 184 























LIST OF PLATES 


Chapter 

L Upper and Lower Case Letters and Al¬ 
phabet of Lines_ III 

II. Details of the 9x12 Sheet_ V 

11T. Drawing Problems Involving Straight 

Lines Only _ VLt 

IV. Rectangular Blocks_ VII 

V. Problems Containing Invisible Lines_ VIII 

VI. More Advanced Problems With Invis¬ 
ible Lines_ VIII 

VII. Chamfered Blocks_ IX 

VIII. Probe ems With Chamfers in Them_ IX 

IX. Two Problems in Bench Woodwork_ X 

X. An Easy Practice Letter Sheet_ XII 

XI. C YLINDRICAL-SHAPED KiXEROISES- XIII 

XIL M ore Difficult Cylindrical Forms_ XIII 

XIII. Cylinder Problems_ XTII 

XIV. Disc Form Problems_ XVI 

XV. More Complicated Disc Forms_ XVI 

XVI. The 10x14 Standard Sheet and An Al¬ 
phabet of Lines_ XX 

XVII. Problems for Case I of Tangents_ XXIII 

XVIII. Two Problems Applying Case V of Tan¬ 
gents _ XXVII 

XIX. Two Other Problems Applying Case V 

of Tangents_ XXVII 

XX. A Nut Bowl Showing Typical Thread 

Drawing_ XXIX 

XXI. A II. S. Standard Machine Bolt_ XXXI 

XXII. Detail Plan for a Oarage_.. XXXV 




















XXIII. Working Details for Same Garage- XXXV 

XXI V. Development Problems_ XLII 

XXV. Three Pyramids and a Cone- XLIII 

XXVI. A Frustum of a Pyramid- XLIII 

XXVII. Problems Involving the Cone- XLIV 

XXVIII. Development of the Truncated Cone__ XLIV 

XXIX. Intersections and Developments- XLV 

XXX. Practical Intersection Problems- XLV 









Mechanical Drawing 

CHAPTER I. 


The Theory of Mechanical Drawing 

A mechanical drawing is a drawing made with instru¬ 
ments in which all of the lines of an object are shown in 
their true relations of length, position and direction. 

The purpose of all mechanical drawings is to so repre¬ 
sent an object that the size and shape conceptions are defi¬ 
nite in the mind of the observer. Most mechanical drawings 
serve only one purpose: to represent the object in such a 
way, that it may be made from the drawing. A photograph 
or a perspective drawing does not always convey true size 
and shape impressions to the person viewing the same. 

All solids are bounded by points, lines, and planes. A 
cube has six equal planes, eight equal lines, and eight points. 
To attempt to represent the different planes of the cube would 
require shades or colors. An isometric drawing of the cube 
would show three faces. A photograph may show three 
faces as a maximum. These faces show in shades or shad¬ 
ows. The extent of any plane is indicated by fines; so that 
an object may best be represented by representing the lines 
of it. The following definition of lines may be of assistance: 

A straight line is the shortest distance between two 
points. 

A line is the path of a moving point. 

A 'line is formed by* the intersection of two planes. 

All intersections of planes on the surface of an object form 
lines. All of the lines of an object must be shown in all of 
their relations. Lines have three comparisons or relations: 
1st, length; one line may be shorter dr longer than another; 
2nd, direction; two lines may run parallel or at right angles 


2 


Mechanical Drawing 


to each other; 3rd, position; one line may be above or below 
the other, the relative position affords a comparison of lines. 
Thus a drawing which shows the true relation of all of the 
lines of an object will give all necessary details, so that the 
object can be reproduced from the drawing, which, after 
all, is the chief purpose of the mechanical drawing. 

“A working drawing is one, from which the object 
drawn, may be made.” This drawing must have all dimen¬ 
sions expressed and must show all materials. 

Mechanical drawing theory is based largely on conven¬ 
tionalities and assumptions. It is not an exact science like 
geometry, but after setting up many conditions, certain 
problems of geometery are often applied. The general ex¬ 
planation of mechanical drawing assumes that space is di¬ 
vided into four quadrants by two intersecting planes, a hor¬ 
izontal or H plane, and a vertical or V plane. The angles 
or quadrants are numbered 1, 2, 3, and 4, beginning with 



1. The H and V planes of projection. 




Mechanical Drawing 


3 


the top front angle and progressing clockwise when viewed 
from the right end. (See Figure 1.) 

An object., when placed in either quadrant will project 
its outline on each of these planes. These outlines become 
the views of the object when the H plane is revolved about 
the line of intersection so that quadrants 2 and 4 are re¬ 
duced to zero degrees, and the H plane coincides with the 
V plane. The method followed in the United States is to 
assume that the object is always placed in the third angle. 
Thus the top projection is found in the H plane and the 
front projection is found in the V plane. When the Ii plane 
is revolved, the H projection or view is turned into a plane 
coinciding with the V plane. The line of intersection and 
revolution is called the ground line, (G. L.) and is drawn in 
the actual representation of these planes. Everything above 
the ground line becomes the H projection and everything be¬ 
low the ground line becomes the V projection. (See Figure 
2 ). 

Several rules are readily formulated from these hypo¬ 
theses. Some rules governing points are as follows: Con¬ 
sider points in the third quadrant. 

1. The H projection of a point is as far above the G. L. 
as the point is back of V. 

2. The V projection of a point is as far below the G. L . 
as the point is below H. 

3. The two projections of a point always lie in a line 
perpendicular to the G. L. 

4. The distance between the H projection of two points 
is always the same as the distance between the V projections 
of these two points when measured on any line parallel to the 

G. L. 

When an object is placed in the third quadrant its pro¬ 
jections are drawn on the H and V planes, the H plane is 
then folded up into the V plane and the II projection be¬ 
comes the top view of the object and the V projection be¬ 
comes the front view. By eliminating the G. L. we have the 


4 


Mechanical Drawing 



ordinary conception of the top and front views of a work¬ 
ing drawing. (See Figure 2.) 


This plan, so far, has not provided for a third view. A 
third or profile plane perpendicular to the G. L. is passed 
to the right of the object and through these two planes. 
This affords a plane on which the end view of the object 
may be projected. By agreeing on the use of the third quad¬ 
rant, and eliminating all extra planes, we have a box-like 


Mg. 2. The object in the third quadrant and its projections on the H 

and V planes. 





M echanicaIj Drawing 


5 


set of three planes. (See Figure 3.) The object is placed 
under the H plane, back of the V plane and to the left of 
the “profile” plane; the three projections are then obtained. 
After the projections are recorded, the H plane is folded 
up into the Vi plane and the profile plane is revolved into line 
with the V plane, using its line of intersection with the V 
plane as an axis. (See Figure 4.) The three views are then 
in these relative positions: 



Fig. 3. The Projection box for finding three views of an object. 

The top view is directly over the front view. 

The right view is directly to the right of the front view. 
Also these results are apparent: 

All lengths are the same in the top and front views. 

All heights are the same in the front and right views. 
All widths are the same in the top and right views. 
The left edge of the right view is the front of the object. 
The lower edge of the top view is the front of the object. 



6 


Mechanical Drawing 


Thus, the representation of the object is a series of pro¬ 
jections of the object or of the lines of the object on planes. 
In some cases the detail of some oblique surfaces of the ob- 



Fig\ 4. The projection box with the three views in the same plane. 


ject are not obtained by these three projections, so that oth¬ 
er planes called auxiliary planes are used in order to de¬ 
termine these true sizes and shapes. (See Chapter 42.) The 
auxiliary plane must be parallel to the surface, the true 
shape of which, is desired. 

Added to this assumption of planes, projections, revolu¬ 
tions and intersections are many conventional methods 
which have been evolved through many hundreds of years 
in the history of drafting. Most of these conventions are so 
well established that their violation would be classed as 
ignorance or presumption. Some of the conventions are 
simply the result of practice. Just as in polite society, to 
eat peas with a knife is a serious breach of etiquette, so to 








Mechanical Drawing 


violate the conventions of mechanical drawing is sim’larly 
an inexcusable practice. 



Fig. 5. A photographic reproduction of a wall hanger. 

Some different forms of graphic representation of ob¬ 
jects are as follows: 

Photographic:—Using a camera, and taking a picture 
of the object. (See Figure 5.) 

Mechanical Drawing:—Two or more views of the ob¬ 
ject with or without dimensions, often shaded or decorated. 
(See Figure 6.) 

Working drawing:—Dimensioned and detailed mechan¬ 
ical drawings made so that the object drawn may he made 
from the drawing. 

Isometric, cabinet projections, etc:—Easy methods of 
near true pictorial representation. (See Figures 134, 136.) 

Perspective drawings:—Exact line drawing reproduc¬ 
tions of pictorial representations (See Figure 130 top.) 

The method of making mechanical drawings from pro¬ 
jections or planes given above, provides for only three 


8 


Mechanical Drawing 


views. Very frequently views from all four sides of the ob¬ 
ject are required. For example in house plans, four eleva¬ 
tions or views, one of each side are required. The roof plan 
is made but no bottom view is drawn; rather a floor plan 
looking immediately down on the floor plane of the house is 
made. Thus it is seen that the student must learn all of the 
conventions of mechanical drawing and observe them very 
closely. 




Fig. 6. A mechanical drawing (not a woi'king drawing) of a wall hanger. 

























CHAPTER II. 


Pencils 


Special pencils are made for use in mechanical draw¬ 
ing-. These pencils are graded by using Hie capital letter H, 
which indicates the degree of hardness of the pencil. Thus, 



Fig. 7. The 4 H pencil used for drawing Ikies. 


1 H pencils are only fairly hard, while 5 H or 6 H pencils are 
very hard. These pencils are made in grades from 1 H to 9 H. 



Fig. 8. Another HHHI4 or 4 H pencil. 


XJse a 4 H pencil for making all lines of the drawing. 
A hard pencil makes more accurate lines when properly 
sharpened than does a soft pencil. It is also true that lines 
drawn with a hard pencil will not rub off or spread and 
smear over the sheet as would happen with lines drawn with 
a soft pencil. The hard pencil will indent the paper; do not 
bear down on it. Draw lines very lightly from left to right 
and from bottom toward top. 

The 4 H or line-drawing pencil should he sharpened 


0 


r 



o 



Fig. 9. Shape to which the 4 H pencil should be sharpened. 

[9] 
















10 


Mechanical Drawing 


wedge shaped and the point should he shaped like a knife 
blade. (See Figure 9.) There are two good reasons for 
this method of sharpening. In the first place, a knife 
point is the ideal shape for accurate line drawing. It stays 
sharp longer than a round point, and its use should result in 
more accurate work. Secondly, two pencils are needed; the 
4 H pencil for line drawing, and the 2 II for lettering. When 
both of these pencils are of the same color, it would be dif¬ 
ficult to distinguish between them if they were both sharp¬ 
ened to a round point. By having the 4 IT pencil sharpened 
flatwise, it is easy to recognize it. 

Use a 2 H pencil for making all letters and figures on 
the drawing. The 2 H pencil is softer and its use in mak¬ 
ing letters is always recommended. This pencil is sharpen¬ 
ed to a long round point. (See Figure 10.) Use a sharp 
pocket knife for cutting away the wood, exposing about %" 



0 i 

Fig. 10. The shape to which the 2 H pencil should be sharpened. 

of lead. Grind this to a round point on a sandpaper pad. 
(See Figure 11.) Do not attempt to cut the lead with the 
knife. It would be best in an elementary class for the in¬ 
structor to shorpen all pencils the first time. 



Fig. 11. A sandpaper pad used for pointing drawing pencils. 

Other types of pencils are numbered in different ways. 
The writing pencils which we use in ordinary work are num¬ 
bered No. 1, No. 2, No. 3, and No. 4. (See Figure 12.) This il¬ 
lustration shows a No. 2 which is the grade we commonly 
use. No. 1 is the softest, and Nos. 2, 3 and 4 are harder. For 












Mechanical Drawing 


11 


sketching work in art classes a very soft and a very black 
pencil is desired. For that work a pencil with a large, round, 



Fig. 12. The writing pencil commonly used is a No. 2 grade. 


soft lead is made. (See Figure 13.) These pencils are grad¬ 
ed 6 B to 1 B, H B and F. The more the number of “B’s” 
the softer and blacker the pencils are. 


Fig. 13. . A sketching or black pencil. 


All drawing or sketching pencils must be kept sharp. No 
great degree of accuracy can be maintained if the pencil 
points are blunt. Keep the sandpaper pad at hand and whet 
the pencil points frequently. 












CHAPTER III 


Lettering Practice 

Tlie first work of any new class should be lettering prac¬ 
tice. The first period that the class reports should be spent 
in practice lettering, following the rules given below. 

Lettering should he done with the aid of 'four hori¬ 
zontal guide lines. In this book, the four gu/le lines will 
be 1/16" apart, making the capital letters 3/16" high and 
the small letters 1/8" high. 

Letters may he either vertical or sloping, hut in either 
case, vertical or sloping guide lines should he drawn. 
At the left in Figure 14 are shown four guide lines with verti¬ 
cal guide lines for aiding in keeping letters vertical. At 
the right of this figure are seen four horizontal guide lines 



Fig. 14. Guide lines :or vertical or sloping letters. 


with slope guide lines. Letters when sloped are made at 15° 
to 30" to the right of the vertical. These are made 15° to 
vertical. This slope has been selected for use in this text, 
and these lines are drawn by setting the 30° angle of the 30°- 
60" triangle on the tee square and then setting a 45° triangle 
on this. These two angles, 30° and 45°, make a 75° angle 
which is 15" less than the right angle. 

The lettering used in this text is unknown as the Rein¬ 
hardt simplified alphabet. The word alphabet is derived 
from the first two letters of the Greek alphabet, Alpha and 
Beta. In English, we call the alphabet, our a. b. c’s. We 
use three general types of alphabets,— upper case, lower case, 
and script. The names, “upper case” and “lower case” 


[12] 













M ECHANICAL DRAWING 


O 


are derived from the type fonts or complete sets of type 
in the printer’s “case.” The printer’s type is carried in 
a flat series of boxes, a complete alphabet in each. For set¬ 
ting type the printer has the lower case box nearest to him, 



Fi:r. 15. The printer’s type storage case showing upper and lower case 
type storage space. 

while the upper case, or capital letter box used more infre¬ 
quently, is further away and over #ie small letter box. Thus, 
the terms “upper case” and “lower case” are derived! 
(See Figure 15) These letters are also called “capitals” 
and “small letters” or “magiscules” and “miniscules.” 
The third type of letters is called script from the Latin 
word meaning written. This is the name given to the 
written characters representing the alphabet. In printed let¬ 
ters we have only the capital and small letters. Figures do 
not have upper case and lower case or capitals and small 
types. The size or height of figures varies with the height 
of upper case or lower case used. 

The Reinhardt upper case alphabet may be divided into 
three groups. The first and simplest group is based on 
straight lines. The second group is made up of full or part 















14 


Mechanical Drawing 


curves. The third group combines these two types. See 
Figure 16. 


ILTF EH K V WZX YNMA 147 


OQGGSSf 09638 


PBRDJU Z5 


Fig. 16. The three groups of upper case letters. 


Ill making letters on the practice sheet, note carefully 
the above analysis as shown by the grouping and by the dot¬ 
ted lines, and use the alphabet shown in Plate I as a guide. 
Upper case letters should be sketched. Note that all letters 
are the same width except the I, M and W. The M is wider 
than the ordinary letters and the W is still wider. 

The lower case alphabet is likewise divided into groups 
on the same principle. The letters of the straight line group 
are formed as those in the top line, Figure 17. The round 
letters are based on an ellipse, the axis of which extends at 


Ifikvwxz 



o oi a o dbpq q 


f fahj ion m/or uy 


Fig. IT. The* four groups of lower case letters. 


Mechanical Drawing 


15 


an angle of 45° to tlie vertical. (See Figure 17). On this 
basis the 0 letters in Fig. 17, are formed. By adding lines 
to the second group letters the third group is formed. By 
combining a part of the curve and straight line, the letters 
in the fourth group, result. 

A closer study of the lower case alphabet shows certain 
relations of letters and parts of letters. 

1. The u is the n bottom side up. 

2. The p is the d bottom side up. 

3. The m is a double n but not quite twice as wide. 

4. The w is a double v but not quite twice as wide. 

5. The y is almost the same as an inverted h. 

6. The i and the j have dots over the letters. 

7. The g and the q are identical except for the direction of 

the tail. 

8. The r is the same as the n with a part of the right up¬ 

right erased. 

9. The f and the j stems are identical when one of them is 

inverted. 

Use the copy given in Plate I for making the lower case' 
practice letters. Spend one or two hours per week practic¬ 
ing lettering. If drawing is studied in the 7th Grade, Up¬ 
per Case letters should be used throughout this grade. 


-LETTERING X L/NES- 
Upper Case 


Lower Case 


Figures 

fpil ifpk 

Lines 


Border Line -— 

Outline Line - 

invisible Line - 

Center Line — 
Cross-section Line 
Projection Line - 
Dimensioning h — 
Break Line 


A 

K 


Plate I. Upper and lower case letters and an alphabet of lines. (Draw¬ 
ing made by L. K. Anderson ) 




















CHAPTER IV 


Drawing Paper. Erasing Pencil Lines 

There are many kinds of drawing paper; the colors used 
chiefly are pure white and cream. For elementary work 
the cream colored paper is to be preferred, because it shows 
erasures and dirt to a lesser degree. There is some varia¬ 
tion in the whiteness of the white paper and in the gloss of 
the surface of white papers. 

Drawing paper may be obtained in rolls and in sheets. 
For convenience in a school course, the paper should be ob¬ 
tained in sheets cut to correct size. Paper is made up in 
standard sheet sizes in thicknesses varying with the size of 
the sheet. The smallest sheets are the thinnest. Standard 
drawing paper comes in these sizes: 


Cap, 

14x17 

inches 

Demy, 

15x20 

inches 

Medium, 

17x22 

inches 

Royal, 

19x24 

inches 

Super Royal, 

19x27 

inches 

Imperial, 

22x30 

inches 

Double Elephant 

27x40 

inches 


The paper for the first group of this series of drawings 
should be ordered 10"xl3%" and may be cut economically 
from the 27"x40" size sheet. By getting the paper from this 
size sheet, a thick and substantial grade of paper is obtain¬ 
ed. The second sheet size is 12"xl5 1 4" and when the 19"x27'’ 
sheet is cut in halves we get a suitable size sheet. When 
paper is mounted it should be perfectly clean. Every pos¬ 
sible precaution should be used to keep it in such condition. 
Drawing paper when sold in sheets is frequently designated 
in reams or quires. 

When lettering a sheet in pencil, use a piece of scrap 



18 


Mechanical Drawing 


paper under the hands to protect sheet. This will frequently 
save the sheet from becoming soiled during this work. 

When drawing pencil lines on the sheet, draw every line 
with the fear that it may have to he erased. Then, if erasure 
is necessary, the sheet will not be indented. Do not bear down 
heavily on the pencil at any time. 



Fig. 18. The ruby eraser, suited to line 
erasing. 

When it is necessary to erase pencil lines, use a re¬ 
liable eraser and erase ■ carefully just Where erasing is 
needed. Sponge erasers are designed for removing dirt 
and not for erasing lines. Use a Ruby or other good make 
of eraser and erase lightly so that the surface of the paper is 
not spoiled. Green erasers sometimes rub off on the paper. 

When erasing a long line , erase next to a straight 
edge similarly to drawing the line. Erasers must be kept 
clean, so that when erasing is needed, the results are satis¬ 
factory. The hands must be clean, but even then, care must 
be taken not to allow the hands to come in contact with the 
paper. 



Fig. 18a. Eberhard Faber No. 100 Pink Pearl is a very good soft eraser 
for line removal. 








.CHAPTER V 


Laying Out the 9x12 Sheet 

The sheet used in the first part of this text finishes 
9 xl2 with a border on all four sides. Each sheet must 
be exactly the same and should be produced as follows: 

Mount the drawing paper on the upper left hand portion 
of the drawing hoard with a thumb tack in each of the top 
corners. 




Fig. 19. Two common types of small drawing boards. 

Figure 19 shows a drawing board made to allow for 
shrinkage. The top face of the board should be smooth and 
clean. This face should be planed and sanded as often as 
is necessary. The left end must be straight. 

When buying drawing paper, do not allow the salesman 
to roll it. Keep it flat at all times; two tacks will then be 
sufficient to hold it in place on the board. Carry the spare 
sheets in a portfolio large enough to insert the paper. 
Home-made portfolios are easily produced. Building paper 
and a cheap riveting machine make their production an easy 
matter. (See Figure 20.) 


[19] 










20 


Mechanical Drawing 



Fig'. 20. A home-made portfolio. 


Several types of thumb tacks may be secured. The type 
where they are sold by the dozen and packed in round tin 
boxes is more suitable for public school use. The tacks 
should be of the small size and should be pressed into the 
drawing board with the thumb. Do not drive them in with 
the tee square. Tliev can be removed by inserting thumb 
and finger nails under edge and twisting the tack. Or insert 







Mechanical Drawing 


21 


a knife blade under the tack lb remove it. A thumb tack pull¬ 
er may be purchased. (See Figure 30). 

After the paper, is mounted the border lines of the sheet 
should be measured off. For this we use the Architect’s Scale. 
There are three words we need to understand: 

A rule is a device for measuring length. It may he 
1', 2', or 3' long. Each inch is usally divided into halves, 
quarters, eighths, and sixteenths. (See Figure 22) 



Fig 22. A one-foot school rule. 

A ruler is a straight hoard or device used for drawing 
straight lines. Usually it has no inch marks on it. (See 
Figure 23) 



Fig. 23. A ruler or straightedge. 

A scale is a device which has a rule on one edge and 
several “scales” on the other edges. Our Architect’s scale 
has three edges, six faces for calibrations and eleven different 
scales. One edge has a 12" rule for measuring inches, halves, 
quarters, eighths, and sixteenths. (See Figure 24). The oth¬ 
er edges have two scales on each, one beginning at either end. 
The scales found on the Architect’s Scale are 3/32" =4', 3/16" 

-r, 14"=r, %"=i', y 2 "-*r> iC- 1 '* 3 " ==1 ' 



Fig. 24. The Architect’s or Mechanical Engineer’s scale. 

The Civil Engineer’s scale, usually called an Engineer’s 
Scale, has a 12" rule on one edge, each inch of which is divid- 
























22 


Mechanical Drawing 


ed into tenths. The other five faces have the inch divided 
into twentieths, thirtieths, fort'eths, fiftieths, and sixtieths. 
(See Figure 25.) 



Fig. 25 . The Civil Engineer’s scale. 


When using scale, mark off lengths on tog edge and 
on left edge of scale. This allows hands to rest on scale 
instead of paper and thus the paper is kept reasonably clean. 

W hen laying off several measurements whose total is 
less than 12", make them without moving scale. This 
tends towards greater accuracy. For example, suppose five 
2" spaces are required. If the scale is moved each time a 2" 
space is laid out, would the five spaces measure exactly ten 
inches? The total length might be over or under 10", while 
if the five spaces had been laid out without moving the scale, 
the total would be exactly 10". 

Do not use the scale for a ruler or straightedge. The 
edges are so thin on the triangular scale that they usually 
become nicked and marred, and few scales are actually 
straight. They are not designed to be used as rulers, or to 
draw lines. 



Fig. 26. A wooden tee square with lined blade. 


Horizontal lines are drawn on top edge of tee square with 
4-7/ pencil from left to right. 











Mechanical Drawing 


23 


The head of the tee square is always held against the 
left end of drawing hoard. These two rules are never v dat¬ 
ed. The tee square is never placed in any other position. 
Lines are never drawn on bottom edge; indeed, some tee 
squares are made with bottom edge cut at an angle, so that 
it cannot be used for line draw ng. (Fig. 27.) The head of 
the tee square is never held on any side of the drawing board 
except the left edge. The board might not be square. 



Fig. 27. A tee square with bottom edge tapered. 


Vertical lines are drawn on left edge of triangle from 
bottom to top. The other edge of the triangle must he in con¬ 
tact with top edge of the square. Because: 

1. Light should come from left front. 

2. Hand does not drag on paper. 

3. Hand drags on triangle and holds it down. 

4. Inking maybe done this way best. 

Either triangle may be used for this. The triangles usually 
furnished for a drawing course are as follows: 

The 45° triangle is one which has one 90° and two 45° 
angles. 

The 30°-60° triangle is one which has one each 90°, 
30° and 60° angle. The sum of three angles in any tri¬ 
angle is 180°. These triangles may be purchased in various 
sizes, those from 4" to 12" being easily obtained. The triangle 
must be held firmly against the tee square for careful work. 
In the better grades of triangles a place is -cut in the inside 



24 


Mechanical Drawing 


edges of triangle to aid in lifting the triangle off the sheet. 
(See Figure 28) 



Fig. 28. The 30°-60° and 45° triangles. 


Do not slide triangle from one part of paper to an¬ 
other. Lift it up and carry it to the other place. This 
aids in keeping the sheet clean. Before starting to draw, the 
triangles, tee square, and drawing board should be dusted 
clean with a dust cloth or a handkerchief. But this is not suf¬ 
ficient. If the triangles are dragged or slid across the sheet, 
dirt is sure to be rubbed off on the sheet. 

Follow this order in laying out the standard 9"xl2" 
sheet. In doing this play a game of solitaire; wager with 
yourself that you Avill not at any time permit any portion of 
your hand or fingers to come in contact with the paper. When 
you are through, count the number of times you have touched 
the paper. 

1. Mount the 10x131/2" paper as indicated in Fig. 29. Use 
2 thumb tacks very close to the top comers. 

2. Measure from left to right in middle of sheet 14 ", V 2 ", 
12", and y 2 . This will leave approximately 14 " waste on 
right. 

3. With nought of Scale at bottom and the 10" mark at 
the 'top, mark the y 2 " point and the 9i/ 2 " point. This lays out 
the 9" sheet and leaves y 2 " borders at top and bottom. If the 


Mechanical Drawing 25 

sheet is not exactly 10", split the difference at top and at hot- 
tom. 

4. Draw the vertical lines first. Since the usual tri¬ 
angle is not long enough to draw all of the vertical line, draw 
the top half of all lines first. The outside lines are trim lines 
and extend to the edge of the sheet. The inside lines are 
border lines and extend to within y 2 " of the edge. Do not 
draw them all the way to the edge, but stop them within y 2 " 
ot the edge. Draw the bottom half of these lines in like man¬ 
ner. 

5. Now draw with the tee square, the top and bottom 
border lines between the inside lines drawn in (4). 



Fig. 29. Drawing the pencil lines laying out the 9x12 sheet. 


Now locate Vines for standard lettering on the inside of the 
9x12 space as follows : 

1. Set scale with nought at bottom and nine at top mar¬ 
gin. Mark off inside of each border line these distances, 1/8" 
1/16", 1/16," and 1/16". With nought at left margin and 
twelve on right margin, mark off y 2 from each margin. 













26 


Mechanical Drawing 


2. Draw the stop lines (2) in Plate II. 

3. Draw the lettering guide lines about 2" long at top 
and entirely across bottom. (See Plate II) 

4. Lay off the middle 4" of t bottom for name of high 
school. 

5. Draw 15° slope guide lines, at each place where letter¬ 
ing is to be placed. 

Put name of high school , in middle 4" of bottom guide 
lines, in upper case letters. 

Put date in lower left corner in lower case letters. Do 
not abbreviate. 

Put your name in lower right , hand corner in lower case 
letters. 

Put Drawing No. 1 in upper right hand corner in lower 
case letters. 

After draw'ng has been completed on the 9x12 sheet, 
put the name of the ; drawing in the middle of top space and 
in the center of the sheet from left to right. 

Lay out i four or five sheets completely and neatly lettered 
so that they will be ready for the drawings to be put on them 
later. Number them: 1, 2, 3, 4 and 5. 




Mechanical Drawing 


27 



Plate II. Details of the 9x12 sheet. 























CHAPTER VI 


Making Preliminary Sketches Before Making 

Working Drawings 

In Chapter I the general principles of mechanical draw¬ 
ing were presented. Before making a working drawing of an 
object it is necessary to make a sketch of the views required, 
put dimensions on this ( sketch and plan the layout of these 
views on the sheet. Otherwise, many mistakes would lie made, 
and in manv cases the, sheet would he so badly laid out that 
it would need remaking. Or if a person is drawing a machine 
part, he 1 would get the sheet very badly soiled if he worked 
directIv from the model. 



Fig. 31. Position of hand and pencil when sketching a horizontal line. 
















Mechanical Drawing 


29 


It is recommended that each student be required to jinake 
a sketch of the problem assigned and have the ^instructor 
check and okeh it before any sheet in this,text is started. A 
few basic rules of sketching are given to aid the student in 
making these preliminary drawings. 

When sketching .a horizonal line, turn the paper slightly 
and hold the pencil at an angle of about 30° to the surface of 
the paper and^perpendicular to the direction of the line. The 
elbow becomes the center of the arc of motion and the line 
is sketched by fragments. , (See Figure 31) 



Fig. 32. Position of hand and pencil while sketching a vertical line. 


When sketching vertical lines, turn the paper slightly to 
right and sketch the line by .a movement of the fingers. The 
hand is moved downward as is needed. This permits the 
student to make very accurate lines. (See Figure 32.) 

When making sketches, maintain the correct proportion 





30 


Mechanical Drawing 


between length of lines. If the problem of sketching a 2 
square is assigned, the four sides should be equal :n length. 
If the problem of sketching a l"x3" rectangle is given, the 
sides should be three times as long as the, ends. 

When sketching circles, draw two perpendicular center 
lines and lay off approximately equal distances from intersec¬ 
tion on these lines. This affords a guide for drawing the 
circle. Start sketching both ways,from each of these points. 
Measure with pencil or piece of paper. 



Fig. 33. Method of sketching a circle. 

Using a sheet 10xl3y 2 " drawing paper, sketch the folio w- 
ing problems: 

1. Draw T a horizontal line five inches long. After it has 
been drawm, measure to see how^ closely you have guessed five 
inches. 

2. Draw a vertical line three inches long. 

3. Draw a 1" square. 

4. Draw T a l"x4" rectangle. 















Mechanical Drawing 


31 


5. Draw an equilateral triangle with sides 3" long. 

6 . Draw a circle having a diameter of 3". 

7. Draw a circle having a diameter of 7". 


CHAPTER VII 


Making the Drawing 

In Chapter I the fundamental basis of mechanical draw¬ 
ing was established. The origin of the three views was ex¬ 
plained and their relative position was determined. Another 
conception of the establishing of the position is now present¬ 
ed. Any object has six directional sides or faces: north, 
south, east, west, top, and bottom. Or stated in another way, 
any object has a top, a front, a right side, a left side, a rear 
or back, and a bottom. Thus, if the six surfaces or faces of 
a bench are drawn (Figure 34) the four showing the height 
may be put in line; the left being naturally placed to the left 
of the front, the right being placed to the right of the front, 
and the back view either to the right or left of these three 
views. Views showing lengths are placed even, so that with 
the front view located, the top is naturally placed over the 
front with the bottom placed below. 


T OF* 









LEn 


' FRONT 


P/6H7 








BOTTOM 



Fig. 34. Six views of a bench. 

It is readily seen that the top and bottom views are al¬ 
most identical, the left and right views are the same, and the 
front and back are duplicates. This gives rise to the rule: A 


r«2i 






























Mechanical Drawing 


33 


mechanical drawing generally consists of three views: the top 
view , the front view, and the right view. The top shows more 
than the bottom, except in house plans (house plans are 
not really bottom views); hence its selection instead of the 
bottom. The right and left views are usually almost the 
same, so there is little choice between them, and the front 
shows more than the back, so it is chosen. 

The top view is always placed over the front view, and 
the right view is always placed to the right of the front. These 
positions, besides having been established in Chapter I, are 
the natural positions. Stand in front of a table or a roll top 
desk. The top is seen over the front; the right is to the right 
of the front. Figure 34a shows three views of a bench where 
an attempt has been made to put the right view to the right 
of the top. Note that this throws this view of the bench 
on edge, which is unreasonable. Therefore, do not violate the 
above rule. In solving the sketching assignment below, follow 
the rules just set forth. 

Using a piece of standard pencil drawing paper, theme 
paper size, sketch the following problems. Sketch each one 
on separate sheets. 


right? 


TOR 


/ FRONT 


righi 





Fig. 34a. Top, front, and right views of a bench. 

1. Sketch three views of a rectangular solid, 2>/ 4 "x4 %"x 
l". The largest surface is the front view. (See Figure 35) 


















34 


Mechanical Drawing 


2. Sketch three views of a rectangular solid, 2 1 /2"x3 1 /2"x 
7"; the largest surface is to be the top view. 

3. Sketch three views of a solid, 3"x3"x5", if the solid 
stands on end. 

4. Sketch three views of the same solid with one end 
as the front view. 

5. Sketch three views of a cube. 

6. Sketch three views of each problem given in Plate III. 



Fig. 35. Three views of a block, 2ty;"x4%"x7". 


In planning the problem (Figure 35) to tit the 9x12 sheet, 
we find that there is 6% inches of drawing vertically for a 
9” sheet. This leaves 214 " for three spaces or %" for each 
space. When we figure lenghtwise we find 9 1 4” of drawing 
with 12" of space or 2%" for three spaces. Put %" in the mid¬ 
dle and 1" for each outside space. (See Figure 35a). With 
this method of planning work we can deduce some rules for 
procedure: 

Spaces at top and bottom should be equal but each should 
be slightly larger than inside space. 










Mechanical Drawing 


35 


Space between top and front and front and right should 
be equal if it is convenient. 







l 

! i. 





0 




0 





V* 

*-- — 1 




Fig. 35a. Method of indicating spacing for the drawing. 

Spaces at right and left of drawings should be equal and 
should be slightly larger than middle space. 

Put amount of space in a circle on sketch. 

When drawing this problem on sheet numbered one, fol¬ 
low this detailed instruction. 

1. With nought at bottom and 9 at top margin, mark off 
3/4", then 4 1 //', then 3/4", then 1 2^4" and %" should remain. 

2. With nought at left and 12 at right margin, mark off 
1", then 7", then then 2y 4 " and 1" should remain. 

3. With tee square, begin at top of sheet and draw all 
horizontal lines, drawing approximately as much of each line 
as will be needed. 

4. With triangle on tee square, begin at left of sheet 
and draw all vertical lines between lines drawn in (3). 

All outside lines of views should be located, the view 
thus being “blocked out,” by drawing light pencil lines. 

After views have been blocked out, heavier pencil lines 
may he drawn over lines representing the views. 


















36 


Mechanical Drawing 


Drawing No. 1—Follow instructions given above and 
make three views of the 2i4"x4y 2 "x7" and block on sheet 1. Put 
name of sheet in center of the upper % space in Upper Case 
letters. Name, “Rectangular Block.” 

Drawing No. 2.—Make three views of any problem il¬ 
lustrated on Plate III. Name the sheet as indicated on this 
plate. 

Drawing No. 3—Draw three views of any problem given 
in Plate IV. 

Notes. Do not dimension any drawing until definitely in¬ 
structed to do so. 

The name of any sheet should be the same as that given 
on the Plate from which it is taken. 


DRAWING PROBLEMS 






Plate II»I. Drawing problems involving visible straight lines. 



































RECTANGULAR BLOCKS 


38 


Mechanical Drawing 



Plate IV. Drawing* problems of rectangular blocks. 




























































CHAPTER VIII 


Invisible Lines 

When all lines are visible in the three views the lines 
representing them are drawn solid. However, many objects 
are drawn that have invisible details. For instance, the rect¬ 
angular solid in the sketch below has a rectangular hole 
through it. (See Figure 36) The top view shows the hole, 
but when the front and right views are drawn, the hole can¬ 
not be seen. 



Fig. 36. A black with a hole in it. Representing invisible lines. 


All lines that cannot he seen and are not covered by a 
line that can he seen are represented hy dotted lines. 

Thus the front view has two dotted lines showing the 
length of the hole and the end view has two lines showing the 
width of the hole. The last dot should touch the line at which 
the dotted line ends. Especially is this true when the drawing 
is inked. Any other procedure will result in poor work. 
(Compare 1 and 2 in, Fig 36). Each dot should be about V 8 " 
long and the space should be 1/16". 

The invisible line is an outhne line, but is made lighter 
than the outline line in most alphabets of lines. For the be¬ 
ginner the invisible line may be inked the same weight as 
outline lines. See Plate I. The advanced student should ink 
it a little lighter. See Plate XVI. 


[ 39 ] 














40 


Mechanical Drawing 


Drawing No. 4. 
on Plate V. 

Drawing No. 5. 
on Plate VI. 


Draw three views of any problem given 
Draw three views of any problem given 



Plate V. Problems containing invisible lines. 






























































42 


Mechanical Drawing 



Plate VI. Problems containing invisible lines. 


























































































CHAPTER IX 


Representing Chamfers 

A 45° chamfer may he drawn in all three views from 
only one measurement. The chamfer is used in many projects 
in woodworking and also in many machine parts. It is used 
for two purposes: first, to relieve and protect the sharp arris 
from indentations and abrasions; second, as an easily produc¬ 
ed decorative effect. Since the new planes forming the cham¬ 
fer make more intersections with the face planes of the solid, 
more lines will be represented in each view. 


_- 

\ '■“<0 .__j 

7 


r 

✓ A ^ 


? —-* 


r -7-s 


£^^ 

2 - g - 




Fig. 37. Drawing a chamfer in three views from one measurement. 


Figure 37 shows a chamfer represented completely in 
three views of a block. To draw all 1 of the lines representing 
the chamfer from one measurement, proceed as follows: 
first, lay out and draw blocking-out lines of the three dews; 
second, make desired measurement, at any point, as 
at a-b; third, draw all 45° lines in top view, of approixmately 
the correct length; fourth, draw a horizontal line through a, 
intersecting the top two 45° lines; fifth, draw two vertical 

[43] 















44 


Mechanical Drawing 


lines through intersections formed in fourth and at same 
time locate points c and d in front view; sixth, draw horizon¬ 
tal line through intersections formed by 3 and 5; seventh, 
draw two 45° lines from points c. and d, locating chamfer in 
front view; eighth, where lines drawn in 7 intersect sides of 
front view, draw horizontal line across front view, and with¬ 
out moving tee square, draw line across right view; ninth, 
draw' the two 45° lines in right view to complete chamfer. 

While it is not essential that all representation of all 
chamfers should be completed by drawing the lines from one 
measurement, it is most desirable that a young draftsman 
should know that it is possible. Much time can be saved, and 
greater accuracy will result if as many measurements as pos¬ 
sible are projected from one view to the others. 

Do not make the same measurement on any two adjacent 
views if it is possible to make it on one and project to the 
othdr. 

By adjacent views is meant top and front, front and right, 
front and left, etc. Thus, it is best to lay off all heights on 
front or right and project to both view's from the one measure¬ 
ment and lay off all lengths on top or front and project from 
these measurements. Transfer measurements from top to 
right by using dividers or by re-measuring. 

Drawing an oblique chamfer requires two or more meas¬ 
urements. ' 1 

Ap oblique chamfer is a flat chamfer cut off at any 
angle not 45°. Both dimensions are usually given. See Ring 
Stake, Plate VIII; the two dimensions in this case are 5/16" 
and 

To draw an octagon having a square given: Measure 
half the length of diagonal back in both directions from each 
corner; connect these points, using 45° triangle for drawing 
lines. Fig. 38. 

Drawing No. 6. Draw three views, top, front and right, 
of one of the chamfered blocks shown on Plate VII. 

Drawing No. 7. Draw three views, top, front, and right, 
of any one of the problems shown on Plate VIIIj 


M EC HAN 1 CAL 1 >RAW IN G 



Fl«;. 3S. Laying out an octagon having a square given. 














CHAMFERED BLOCKS 


46 


Mechanical Drawing 



Plate VII. Chamfered blocks. 
































































































Mechanical Drawing 


47 



Plate VIII. Problems containing chamfers. 


























































































CHAPTER X 


Round Holes in or Through a Solid 

A round hole in or through a solid is represented by a 
circle in one view and by invisible or dotted lines in the other 
views. Round holes are generally made by boring with auger 
b.ts or with drill bits, though in sheet or plate metals, they 
may be punched. For the purpose of centering the bit or 
drill, the center of the hole must be located first. The center 
of the circle is a point. A point can best be located by two 
intersecting lines. 

The center of a circle must always be located by two in¬ 
tersecting lines. These lines are most frequently at right 
angles but may intersect'at any angle. The type of line used 
is the center line. 

Study the problems involved in drawing three views of 
a block with a hole through the center of it. (See Figure 39.) 



Fig. 39. Locating and representing a hole through a block. 

In the method employed in this drawing, the center of the 
circle is located by drawing the two diagonals of the rectangle. 

The center of a rectangle may be located by drawing 
the diagonals. The center is the point of intersection of the 
diagonals. After the diagonals are drawn, the circle of the 

[48] 








49 


Mechanical Drawing 

desired diameter is drawn. Circles are drawn with a compass. 
Hie usual drawing set lias a compass made up of several 
’parts. As shown in Fig. 40, they are: 1. Compass with di¬ 
vider points; 2. Pencil attachment; 3. Inking attachment; 
4. Extension bar for drawing large circle. 

r lhe lead of the compass should be sharpened by grinding 
it on a sanding pad as indicated in Fig. 43. In adjusting the 
pencil compass for drawing circles, be sure that the lead and 
metai points are even, or that they are the same length. 



When setting the compass to size, set the metal point in 
any inch mark on the scale and then set the pencil point in 
the calibration representing the correct distance. (See Figure 
41). 

In drawing a circle with pencil or with ink, move the 



Photo 41. Setting compass to size prior to drawing a circle. 



























50 


Mechanical Drawing 


point clockwise in direction. Grasp the knurled or ribbed 
point of compass between thumb and first finger of right hand. 
Guide the metal point of one leg of compass to correct point 
formed by two intersecting lines, press the metal point lightly 
into the paper and draw circle by leaning top of compass for¬ 
ward and allowing weight of leg containing pencil point to 
drag on paper. 



Photo 42. Method of drawing circle. 


For small circles, the bow compass is provided. This is 
made in two separate compasses (See Fig. 43), one for pen¬ 
ciling and the other for inking. In Figs. 39 and 44 after the 
circle is drawn in the top view, the sides of the hole are locat¬ 
ed in the front view by projecting from the sides of the circle 
in top view. The sides of thd hole in the right end view may 
be measured. 

Two center lines are always used to located the center 
of the hole, or circle. These center lines should be drawn so 
that they extend beyond the circle about y 2 ". The centers of 








Mechanical Drawing 


51 



all holes through the other views are located by center lines 
extending y 2 " outside the view. (See Figure 44.) 




Fig. 44. Showing correct use of center lines, when representing a hole in 
or through an object. 

Drawing No. 8. Draw two, views of any problem not al¬ 
ready drawn from Plate VIII. (Do not dimension.) 

Drawing No. 9. Draw two views of either problem on 
Plate IX. 








Plate IX. Shop Models. 


































CHAPTER XI 


Inking the Letters on the Sheet. 

After five or six sheets have been completed in pencil, 
time may be taken for a study of inking the letters on the 
drawing. In order of inking found in the Chapter XV it is 
seen that letters may be inked first or last. As the classwork 
progresses some students will complete their work faster than 
others. These may be set to inking the letters on sheets al¬ 
ready finished. 

For inking letters a rather fine pen is used. The Gillott 
No. 303 is recommended as being suited to this type of draw¬ 
ing course. The sheet need not be fastened to the board but 



Fig. 45. Gilloit lettering pens. 


should'be turned to a convenient position so as to facilitate 
inking. The ink used should be some type of water proof 
black or Indian ink. There are several brands of drawing 
ink, but all of them come in similarly shaped bottles. The 
stopper of the bottle has a quill projecting from its center 
into the ink. The bottle should be fastened down on the draw¬ 
ing board or table to prevent its being spilled by being upset. 
The pen staff should be fairly small, so that if it is pushed 
into the bottle it will not rub against walls of bottle neck. 
The new pen should be smoked so it will retain ink. It should 
not be heated red hot because this will draw the temper. The 
lettering pen should he filled with the quill in the bottle stop- 

[53] 











54 


Mechanical Drawing 


per. It should not be dipped into the ink bottle. (Fill it same 
as for a ruling pen, see Figure 55a). Hold quill and pen 
over the bottle so that any stray drops of ink will fall into 
the bottle. 



Fig. 40. Water-proof drawing ink. 

After the pen is filled with ink, a medium sized drop be¬ 
ing held on the lower face of pen,the letters are inked. When 
inking wdth lettering pen, follow these general rules: 

All vertical or slightly sloping lines are inked with one 
stroke, from top to bottom. (See Figure 47). 



Fig. 46. Thin pen staff for lettering. 


All horizonal lines are inked from left to right. 

All circular letters and figures are inked with two strokes, 
the first beginning at top right hand and finishing at bottom 
left hand corner, the second stroke beginning at top right 
and proceeding downward to complete the letters. All par¬ 
tial circular letters and figures are completed the same way. 

All parts of letters must be of same Weight. 

Do not use a blotter overfletters after they have been 
inked. Allow ink to dry and it will be blacker and more 







Mechanical Drawing 


55 


permanent. Do not attempt to erase guide lines until sev¬ 
eral hours of time have elapsed. Then erase very lightly 
with point of eraser. Do not rub over letters until the ink is 
partly removed. Guide lines should be easily erased; then the 
letters will not be dimmed in the process of erasing. 



23 

Fig. 47. Order of strokes in inking letters. 

.The lettering on all of the sheets drawn up to this time 
may be inked before more sheets are made, if it is found de¬ 
sirable to do so. 


CHAPTER XII. 


Letter Sheet. 


A formal letter sheet affords good practice in penciling 
and inking freehand letters. The letter sheet; should not be 
too complicated but the product should be an accurate gage 
of the ability of the student. In a mechanical drawing course, 
no work should grade under 90%; indeed it should be even 
better, for acceptance. The learner must make sheets over 
until they are worth' at least 90%. By keeping the difficulty 
of the assignment within the ability of the student, this 
standard of accuracy may be maintained. 

Practice lettering pads may be obtained from publishers 
and manufacturers of drawing instruments. (See Figure 48.) 
These pads are most frequently lined with three guide lines, 
the bottom space being twice as large as the top. Another 
size of lower case is made by making this bottom space 3/32" 
and the top space equal to half of this amount. 

Two letter sheets are given, Plate X and XVI. One is 
to be made at this time in the course; the second is to be made 



Fig. 48. Practice lettering guide sheet pad. 


at the beginning of the second term or year of drawing. It is 
a splendid practice to start each term’s work with a letter 


[56] 
























Mechanical Drawing 


57 


sheet. The second letter sheet includes a simple type of block 
letters and it should be made oidy after more experience has 
been 1 gained by the student. 

There are many kinds of mechanical letters. Those made 
on squares laid out on the paper are called Block Letters. 
The simplest form of block letters is the one five blocks high 
and three blocks wide. All corners are cut off at 45° and 
slope lines are all of a uniform slope. The letters i, m, and 
w, are one, four, and five spaces wide. When the a and v or 
w are adjacent, the space is closed up one space. The block 
letters may be outlined, inked solid or shaded 45° to top right 
or bottom right. 

Block letters or other forms of mechanical letters are 
used on display drawings and cover sheets. Ability to do fine 
decorative lettering requires and denotes a considerable ar¬ 
tistic ability. 

Drawing No. 10. Lay out the letter sheet as indicated 
on Plate X. The guide lines and slope lines must be drawn 
very lightly. If they are heavy, dents 1 will show in the paper 
after the erasing is done and in erasing, the letters themselves 
will be blurred. Fill the first and fourth lines from left 2" 
border to right 2" border with Upper Case alphabets; the sec¬ 
ond and fifth with Lower Case alphabets and the third and 
sixth with figures and fractions. In the last line, print in 
lower case letters a motto such as: “ The ability to do good 
lettering may be gained by practice. ’ ’ The name of the sheet 
lettering is placed in the top space. . 


58 


Mechanical Drawing 



Plate X. An easy practice letter sheet 

























































CHAPTER XILI 


Cylinders 

Rectangular solids have six views. Cylindrical solids 
likewise have six views. It is more difficult to visualize these 
six views, but if card nal directions are used, we have North, 
South, East and West; then top and bottom, giving us six 
directions for looking at the object and thus six views. In 
figures 49 and 50 are shown six views of a cylinder, first with 
axis vertical, and second with axis horizontal. 


1 

© 



Ltf-f 


front' 


R.ght 


Hear 



) 



Fig. 49- The six views of a cylinder when the axis is vertical. 

In either case, it is observed that one shape is repeated 
twice and the other is repeated four times. This makes it un¬ 
necessary to draw all six views. Even three views would re¬ 
peat certain shapes twice, so that this rule may be given: 

A cylinder may be represented by two views. When the 

[59] 






60 


Mechanical Drawing 


axis is vertical, draw the top and front views; when the axis 
is horizontal , draw the front and right views. (See Figure 

51.) 



Cylinders are formed in several ways. In considering 
geometrical cylinders, a plane l"x5" when revolved about one 
of the long edges, forms a 2"x5" cylinder. Or a 2" circle, if 
moved 5" in a direction perpendicular to its surface, will form 
a 2 x5' cylinder. In the shop, cylinders may be turned in the 
lathe. The rough stock is turned to a perfect diameter and 
the ends are cut square. Shafting and wire are formed by 
soft metal being forced or drawn through a round hole. How¬ 
ever, the most common conception of a cylinder carries with 
it the idea of revolutions about an axis. The earth revolves 



Fig. 51. Two views of a cylinder shown in two positions. 

















Mechanical Drawing 


61 


on its axis, the axis of rotation passing through the north 
and south poles. The axis or revolution is present in drilled 
holes, cylinders of engines and in many types of cylindrical 
forms. 

The axis of revolution of a cylinder is always drawn and 
is represented by long and short dashes. This line is called 
the center line. 

The end view of a cylinder is always a circle. The cen¬ 
ter of this circle is always located on the drawing by two in¬ 
tersecting center lines. 

The preliminary sketch of the cylindrical form drawing 
should show the proper selection of views and also the correct 
use of center lines. Figure 52 shows a hollow cylinder of 
which the front and right views have been sketched. After the 



sketch is made and dimensions are placed on the sketch, the 
spacing should be figured. In addition to the regular spacing 
as has been figured for earlier sheets, the, distance to all cen¬ 
ter lines from the nearest border line must be given. 

Indicate distances from all center lines to the nearest 
border line by dimensions in a circle. The sketch shown in 
Fig. 53 is of the correct type. When the student has the 
sketch this far along, the instructor should check it and okeh 
it so the pupil can proceed with the drawing. 

The order of drawing the pencil lines on a drawing of a 
cylinder is very definite. Center lines should be located rath- 





















62 


Mechanical Drawing 



Fig. 53. The same sketch showing the amount of spacing and location of 

center line. 


er than the edges of circles. Figure 54 shows the order of 
drawing the pencil lines of the drawing shown in the sketch 
solved in Figure 53. The procedure is as follows: 

1. Locate position of horizontal center line by measur¬ 
ing 4 y 2 " down from top border line. 

2. Locate the two vertical lines in front view and the 
vertical center line by measuring iy s " and 6 1 / 4: " from left bor¬ 
der and 2%" in from right border line. These measurements 
should be made without moving scale. 

3. Draw pencil lines 1, 2, 3, and 4 in this order. Draw 
center lines of long dashes and short dots. 

4. Draw the two circles. 

5. Project from top and bottoms of circles as indicated 
by the arrows and draw lines 7, 8, 9, and 10. 

Any great divergence from this order of drawing the 
pencil lines of this drawing will result in loss of effort. Any 































Mechanical Drawing 


63 


l 



Mg'. 54. Cider of drawing lines of diawlr.g <.f a hollow cylind-. o. 

time spent in locating lines 7, 8, 9, and 10 by measurement is 
wasted. Similarly, time consumed in locating the edges of 
the circle is largely lost. Furthermore, in all drawings of 
cylindrical shape, it is best to follow this order of proced¬ 
ure. This is undoubtedly “the one best way.” 

Drawing No. 11. Draw two views of any problem on 
Plate XI. 

Drawing No. 12. Draw two views of any problem on 
Plate XII. 

Drawing No. 13. Draw two views of any problem on 
Plate XIII. 
















CYLINDRICAL FORMS. 






Plate XI. Cylindrical shaped problems. 
































































































Mechanical Drawing 


65 



Plate XII. More cylindrical forms. 























































































































66 


Mechanical Drawing 



Plate XIII. Cylinder problems. 




















































































































C HAPTER XIV 


Dimensioning 

The purpose of dimensioning the drawing is to make it 
possible for the workman to make the object from the draw¬ 
ing. Therefore, all necessary dimensions must be given and 
with great clarity and accuracy. The following rules are given 
as a help in dimensioning the drawing: 

1. Place dimensions below and to the right of the views 
when possible. 

2. Place an equal number of dimensions on each view 
when possible. 

3. The first dimension line shoidd be at least 14" from 
the drawing and other dimensions should be the same distance 
further away. 

• 4. Termination lines should not touch the drawing. 

Leave a space of 1/16". 

5. Termination lines should extend y 8 '‘ beyond the last 
dimension line. 

6. Figures should read from bottom of sheet on all hori¬ 
zontal dimensions and from the right end of sheet when di¬ 
mensions are vertical. 

7. The bar of all fraction should be in line with the di¬ 
mension 1 line and should be inked with the ruling pen when, 
dimension line is inked. 

8. The number of degrees in an angle should be given 
in an arc of a circle. 

9. Arrow tips shoidd be sharp but not too long or con¬ 
spicuous. (Arrow tips may be inked with ruling pen and tri¬ 
angles, sides of arrow forming an included angle of 30°. 

10. Termination lines should never cross dimension lines 
and vice versa. 

11. Angidar distances must be given on a radius of a cir¬ 
cle. (See 1%" Plate XIX.) 


[071 


68 


Mechanical Drawing 


12. Dimension lines and center lines should never co¬ 
incide. 

13. Figures should not he placed on a center I line. 

FINISHED COGS 




Pig. 55. A commercial drawing from a MEDART catalog showing the plac¬ 
ing of dimensions and dimension lines. 


Figure 55 shows two drawings from a Medart catalog 
with dimension linesl placed for customer to fill in. Note that 
termination lines touch the drawing. Also that lines connect 
the views. Our rules of dimensioning do not advise these 
























































































Mechanical Drawing 


69 


methods, yet this is a splendid example of commercial draw¬ 
ing. 

In Figure 56 two drawings are shown hearing out most 
of the rules given above. Figure 57 shows a drawing in which 
several rules of dimensioning are violated. Figures on vertical 



Fig. 57. A drawing poorly dimensioned. 


dimensions do not read from right. This rule is not so in¬ 
violable as some others. The bars of the fractions are not in 
line with the dimension lines so that 1-1/16 might be mistaken 
for 11/16 or 13/16 might be interpreted as 1-3/16. 

Mo. / Morse T<*£>er. 



Figure 58 shows a drawing taken from a South Bend 
lathe instruction book which is well dimensioned. The bars 
of fractions have been made freehand and vertical dimensions 
read from the bottom but these are not severe mistakes. 

Figure 59 shows the correct method of dimensioning cylin- 












































70 


Mechanical Drawing 


der drawings for this text. All rules of dimensioning are 
observed. 

Drawing problem. Dimension at least four of the six 
sheets previously drawn. 


CHAPTER XV 


Inking the Drawing 

This is a very important part of the work of making a 
drawing. Pencil drawings are frequently made and'are not 
inked, the drawing being worked from by the craftsman. This 
occurs in cabinet and mill works where full size details are 
often made for the use of the worker. On the other hand, 
many drawings are made ini pencil and tracings are inked di¬ 
rect from the pencT drawings. This is true of all work 
where several sets of blueprints are necessary for competitive 
bids. In such cases the pencil drawing is not inked. But in 
most school work all pencil drawings are inked. This gives 
the student inking practice for later work in making tracings. 

The instruments most commonly used for inking are the 
ruling yen and the inking compasses. Ruling pens come in 
several sizes, all sizes being used essentially the same way. 
It is best to practice'drawing lines on scrap paper. 




Fig. 59. Two sizes of ruling pens. 

Fill the ruling pen hy touching the quill in the stopper to 
the inside part of the points of the ruling pen. Hold the lit¬ 
tle fingers of the two hands together. Hold the ruling pen in 
left hand and the bottle stopper in right. (See Figure 59a). 
Do not fill the pen too full. Do not fill the pen over the sheet; 
the correct place is directly tover the bottle. Do not put any 
ink on outside of nibs of ruling pen. If any ink should be dis¬ 
covered on the outside, wipe it off with soft cloth. Do not 


[71J 









72 


Mechanical Drawing 


leave stopper out of bottle. The ink solvent will evaporate 
rapidly. The ink bottle should be fastened to table to keep 
it from upsetting. 



Fig. 59a. Filling a ruling pen. 

Lines are always inked from left to right on top edge 
of the square and from bottom to top on left edge of tri¬ 
angle. The screw head of the ruling pen is always held on 



Fig. 60. Inking horizontal lines with ruling pen. 











Mechanical Drawing 


(6 


the outside of the straightedge. The pen is held - perpendicu¬ 
lar to the paper, but leaning in the direction of motion. 

Ink all lines of the same weight before changing setting of 
ruling pen. Thus, all border lines are inked, then all outline 
lines of the drawing and then all of the lighter lines. In this 
text only three weights of lines are given. Many texts g've 
four and some give more than four. In many texts the invis¬ 
ible lines are somewhat lighter than outline lines, yet invisible 
lines are outline lines and may be made the same weight. 
Each drafting room has its own rules about weight of lines, 
conventions, etc. 



Fig. 61. Inking vertical lines with ruling pen. 


Lines are always inked from left to right on top edge 
represent different things in mechanical drawing. A complete 
set of lines with an explanation is called an alphabet of lines. 
The order of inking lines should be as follows: 

1. Border lines. 

2. Circles and arcs of circles. 

3. Irregular curves. 

4. Horizontal outline lines, beginning at top and inking all 

horizontal outline lines including invisible lines. 

5. Vertical outline lines, beginning at left and inking all 





74 


Mechanical Drawing 



vertical outline lines, including invisible lines and pro¬ 
ceeding toward right. 

6. All oblique outlines. 

7. All horizontal dimension, termination and center lines. 

8. All vertical dimension, termination and center lines. 

9. All cross section lines. 

10. Lettering. (This may be done first if desirable.) 

When inking circles, set the point of the compass the 
same length as the pen. Fill the pen and try drawing a circle 
on scrap paper the same size as the required circle. When 
the circle is large, v bend the two legs of the compass so that 
they are parallel. Always ink circles in a clockwise direction, 
holding the compass by the knurled 'tip. (See Figure 62). 
Let the weight of the compass be the pressure applied. 


Should smears or'blots result, the sheet should be made 
over. No erasing of ink is permissible. In case ink is to be 


Fig. 62. The position of compass and hand when inking a circle. 








Mechanical Drawing 75 

removed a sharp round-pointed knife is used and the ink is 
shaved off. This is not to be encouraged. It is better not to 
make mistakes. 

'After inking has been done, let the sheet dry for several 

hours before cleaning. 
Erase all extra pencil 
lines with high grade 
pencil eraser, then clean 
sheet with some soft 
cleaning eraser. (See 
Figure 63). Do not rub 
hard on the paper, and 
the inked lines will not 
be dimmed. After the 
sheet has been cleaned, trim it and file it away. 

Drawing* problem. Ink all sheets made to date. Should 
blotte be made, make the sheet over. Do not ink lettering, 
guide or slope lines. 



Fig. 63. A parent cleaning eraser. Not used 
for erasing lines. 









CHAPTER XVI 


Disc Forms 

Disc forms are short cylinders. Take the problem of 
drawing two views of a 6" ring made of'l" square stock. This 
is really a 6" cylinder 1" long and all of 1 the principles involved 
in the cylinder problems in Chapter XIII will apply. • 

Many disc forms have holes in groups of two, three, four, 
six, or eight, equally spaced about a circle. These'holes are 
located by drawing a complete circular center line and then 
drawing 1 radial center lines across this circle. The radial cen¬ 
ter lines should project %" beyond the circle representing the 



[ 76 ] 






























Mechanical Drawing 




77 


hole. When these holes are spaced equally there is ! no need 
for dimensioning the angle of spacing. 

Note the method used in dimensioning the disc form 
drawn in Figure 64. 

Drawing No. 14. Draw two views of any problem on 
, Plate XIV. Dimension the sheet. 

Drawing No. 15. Draw two views of the truck wheel 
shown in Fig. 65. Table of various sizes will be found below 
the figure. Dimension the sheet. 

Drawing No. 16. Draw two views of any problem on 
Plate XV. No dimensioning. 


















78 


Mechanical Drawing 



5HEAVE PULLEY ELY WHEEL 




























































Mechanical Drawing 79 



Plate XV. More difficult disc forms. 


















































































































CHAPTER XVII 


Scale Drawing 

When an object is too large to be drawn its actual size 
on the sheet, it must be drawn to scale. For instance, two 
views of the library table Fig. 69 are to be drawn. The 
amount of drawing lengthwise of the sheet is 44 plus 28 or 
72”. This is to be put in a 12” space. The drawing could be 
made 1/7 or 1/8 size. 

There are two standard scales used. 1. In architecture a 
certain part of an inch is allowed to equal one foot. 2. In 
shop drawings frequently a fractional part of an inch is al¬ 
lowed to equal one inch. Strictly speaking, the regular scale 
is designed for use as indicated in (1) only. 


(! 

ippfPT | T" 

; | 10 

1 1 1} 1 1 “I] 

P° rrm N 


n? 

K-/A- -*1 

FT 

‘- 6-ICh - 

y{ 

—Q ^ WETZGEK 

j 

. 1 ze , I 88 1 t8 I 

,!,!,] 1 1 1 1 1 1 1 1 1 1 1 I 

1 8 1 01 I 5,1 I *1 I *>„. 1 ‘Vas | 

rH 1 h\ 1 1 1 i 8 rl 1 iVi hlii ilJ 

H.ftUTl.TwTl 


Fig. 66. A scale with four eommon scales on it, used by architects. Also 
with the distance 6'-10" indicated on two* scales 

Figure 66 shows a style of scale used by architects which 
has four scales on the top edges: 1/8”=1' 14" = 1', 
and 1" = 1'. Each of these scales except the smallest has the 
end space divided into twelfths so that feet and inches may 
be measured. O11 this scale, the distance 6 -10” has been in¬ 
dicated on both the 14"=1', and the %"=1' scale showing the 
use of the spaces representing feet and the one space divided 
to allow inch measurements to be made. 

Consider the two views of the built-in book case, Figure 
67. The entire length of drawings is 13'-1" and the height is 
7 -11”. Using* the scale the 9"xl2” sheet size becomes 

12x16', leaving spacing as indicated on Figure 67. The archi- 

[SOJ 














Mechanical Drawing 


81 


tect usually uses a large sheet of paper and makes his draw¬ 
ing to a convenient scale, then draws a border outside the 
drawing. He seldom uses a standard size sheet. A drawing 
of the floor plan of a large high school measuring 82'xl76' 


tit, A 

/ 

6 4* 

<<■'/ 

r/4 * 4 

4 ' t fa 





-IO'-lCh 




fr 1 * 




h L 


© 


'S/leeJ jSac 3~X/Z' on sca/e, 'x./6‘ 


Fig. 67. Spacing, for 2 views of built-in bookcase, scale, %"=!'. 


feet might be made on a scale of 3/16" = T or the size of the 
drawing would be 15%"x33”. The draftsman, however, 
would never figure this size, simply taking a sheet of paper 
large enough to hold the drawing. 

Architectural drawings or plans usually consist of sev¬ 
eral sheets. When the sheet size is determined, all of the 
different sheets are usually made the same size. In order to 
facilitate the making of a drawing to scale, a scale guard, 


Fig. 68. 



A triangular scale guard, used when making a scale drawing. 





















































































82 


Mechanical Drawing 


(Figure 68) is clamped on the scale. This keeps the scale in 
use oii the bottom and aids in speeding up the work. 

Shop drawings are frequently made, allowing some in- . 
tergal part of one inch to represent one inch. The table on 
page 83 shows the proportionate size of the drawing for 
architectural and shop drawings. In the architectural scales, 
the proportionate sizes 1/12, and 1/16 are the only 

ones usable for drawing shop models. On the shop scales, the 
additional scales, 3/32, 3/16, %, V 2 an( i 3 4 sizes are made 
available. It is apparent from a close examination of the 
scale, that it was not designed for this use, but many drafts¬ 
men and teachers are using it. Examine any issue of Manual 
Training magazines and almost half of the drawings are 
labeled Scale 3/8"=l" or 3/16" = l", showing that this is 
common usage. 

In figuring the spacing for two views of the library table 
shown in Figure 69, it is found that there are 72 of drawing 



Fig 69 Two views of a library table, drawn on 9x12 sheet to the scale 

y 8 "=i". 






























Mechanical i )ra\ving 


83 


lengthwise ot' the sheet. By referring to the table on this 
page under “Shop” the nearest sheet size is 72x96 using the 
scale 1/8" = 1”. So in figuring the location of views we find 
the spacing as indicated in Figure 69. In making the draw¬ 
ing, always use the " = 1 " scale for making all measure¬ 
ments. 

Always designate the scale of a drawing unless it is made 
full size. It seems superfluous to write scale full size on the 
sheet, but some authorities recommend his. Always write 
out the full phrase, Scale %" = 1 " or Scale 14 " = !'; never say 
%" Scale or 14 " Scale 

Table giving size of sheet and proportionate size for the 
ten different scales. 


Scale 

Architectural 

Scale I 

Shop 


Proper- 

Size of 

Size of 


Propor- 

Size of 

Size of 


donate 

9x12 

19x14 


donate 

9x12 

10x14 


size of 

Sheet 

Sheet 


size of 

Sheet 

Sheet 


draw. 




draw. 



3/32=1' 

1 /12S 

96x128' 

80x112' 

3 /32''=1" 

3/32 

96"xl28" 

80''xll2" 

1/8=1' 

1 /96 

72x96' 


1/8"=1" 

1/8 

72"x96" 


3/16=1' 

1/64 

48x64' 

40x56' 

3/16"=1" 

3/16 

48''x64" 

40"x56" 

1/4=1' 

1/48 

36x48' 


1/4"=1" 

1/4 

36"x48" 


3/8=1' 

1 /32 

24x32' 

20x28' 

3/8"=l" 

3/8 

24"x32" 

20''x28'' 

1/2=1' 

1 /24 

18x24' 


1/2"=1" 

1/2 

18"x24" 


3/4=1' 

1/16 

12x16' 

10x14' 

3/4"=l" 

3/4 

12''xl6" 

10"xl4" 

1"=1' 

1 /12 

9x12' 


1"=1" 

Full size 

9"xl2" 


iy 2 =T 

1 /8 

6x8' 


iy 2 "=i" 

IV 2 size 

6"x8" 


3=1' 

1/4 

3x4' 


3" = 1" 

3 times 

3"x4'' 





. 


full size 




Drawing No. 17. Make a scale drawing of some piece 
of furniture in the shop. A library or study table or the 
drawing table will be acceptable. 

Drawing No. 18. Make a drawing of a built-in cupboard 
similar to the one shown in Figure 67. A kitchen cabinet from 
some standard mill works catalog will answer. 

























CHAPTER XVIII 


Making Tracings 

Tracings are made so that any number of additional blue¬ 
print copies of the drawing may be obtained. The making of 
blueprints from tracings permits the preservation of the orin- 
inal drawing or tracing. In case of competitive bids, all bid¬ 
ders work from identical drawings or prints. 

There are two kinds of material used for making tracings. 
Tracing cloth is a very fine linen cloth fabric coated with a 
transparent starch material. This is very strong, and will 
stand rather hard usage and some erasures. It will not resist 
wrinkles when doubled, and it will show water spots if water 
should touch it. This material is very expensive, but is widely 



Fig 70. Tracing cloth or paper in sheet form, with border and title space 
printed on sheec. 






































Mechanical Drawing 


used, especially where there is a possibility that many prints 
will be made from the copy. 

The second material used is tracing paper. This comes 
in several varieties, white or cream, oiled or tissue, and heavy 
or 1 ght. It is in no way as strong or as permanent as tracing 
cloth, but it is relatively very much cheaper. It is entirely 
satisfactory when only a few prints are to be made. Archi¬ 
tects use it very largely. Students when first attempting to 
make tracings should use tracing paper. After greater ac¬ 
curacy is attained, tracing cloth may be used. 

Tracing cloth and paper usually have one glazed surface 
and one dull surface. There is some difference of opinion as 
to which side should be inked. The majority of authorities say 
that the unglazed side should be used when inking. Chalk 
dust or talcum powder is sometimes rubbed over the surface 
to cause the ink to adhere more easily. Extremely great care 
must be taken when making a tracing. No erasing should be 
pern issible. Erasing will always injure the tracing cloth or 
paper. 

Inking the original drawing is not necessary before mak¬ 
ing a tracing. In fact, this wall be time wasted. If the draw¬ 
ing is to be traced, the pencil lines should be slightly heavier 
than they are usually made. Stretch the tracing paper or 
cloth over the drawing, using one tack at each corner. Finish 
the tracing before removing the work from the board if pos¬ 
sible. 

Draw in the outside or trim lines on the tracing with a 
soft pencil. The top and bottom guide lines for letters may 
be drawn with a soft pencil and thus aid in keeping the letter¬ 
ing in exact line. Soft pencil lines may be erased without 
seriously injuring the material. 

Cleaning of tracing with sponge or other forms of clean¬ 
ing erasers should be unnecessary. Follow the same order of 
inking when making the tracing as was given for inking the 
drawing. Tracing paper and cloth usually come in rolls of 
varying lengths and widths. Frequently, however, this ma- 


DETAIL or BR LAST OR ill 


86 


M ECHANICAL DRAWING 
















































































































































































Mechanical Drawing 


87 


terial may be obtained in sheets. Firms adopting standard 
sized sheets have the border and title space printed on the 
sheets. (See Figure 70.) One advantage in having standard 
sheet size is the ease of filing. 

Drawing Problem. Make tracings of at least two of the 
last live drawings previously made. 




































CHAPTER XIX 


Making Blue Prints 

Blueprints are made by exposing a sensitized paper , under 
a tracing, to the sunlight or to a strong artificial light for a 
definite time , then washing the print to fix the copy. The proc¬ 
ess is similar to that followed in printing a photograph from 
a negative. The tracing takes the place of the negative. The 
paits of the blueprint paper covered by the lines on the trac¬ 
ing wash out white, while all of the background or the parts 
affected by the sun become a deep blue color. 

Blueprint paper comes in rolls, 24, 30, 36, 40, etc. inches 
in width. It is carefully wrapped in light proof coverings. 
It must be kept away from the light, and deteriorates rapidly. 
A test for blueprint paper may bo made as follows: tear off 
a small piece of paper from Ihe new roll; wash it in clear 
water. It should wash out a clear white. Expose a small 
piece of paper to the sun for 30 to 45 seconds. Wash this, and 
it should become a deep blue. Blueprint paper should be 
kept in a tin or pasteboard tube when not in use. The wide 
roll may be sawed into rolls of convenient widths with a hand¬ 
saw. For the 9x12 sheets, buy a 32" roll and saw it into 
thirds. 



Fig. 73. A tube in which the blueprint roll may be kept. 


When making a blueprint, take the back out of the print¬ 
ing frame. Clean the glass thoroughly, being sure that it 
is dry. Place the tracing on the glass with the inked side 
next to the glass. Over this spread the blueprint paper with 
the sensitized side next to the tracing. Then lay the felt pad 
over the blueprint paper and insert the back pieces. Expose 


[ 88 ] 


Mechanical Drawing 


89 


the frame to the direct, rays of the sun. These rays should 
strike the glass perpendicularly. Do not attempt to hold the 
frame inside glass windows or screwed windows. Time the 
exposure carefully, using a watch with a second hand and 
giving the print about 30 seconds. Remove one end-piece and 



Fig. 74. A well-designed printing frame. 


examine print. The lines will appear dully. Give the print 
a few seconds more exposure, then remove the blueprint paper 
and wash quickly in a bath of pure, clean water. Allow print 
to stand in the water for a few minutes; then hang on a line 
to dry. Be sure to dry the print inside, not in the sun. Do 
not allow any water to splash on the printing frame or tracing. 

Blueprint paper is now made so that no chemical is need¬ 
ed in the bath. For many years, certain chemicals or fixers 
have been added to the bath water when washing the blue¬ 
print. This may be done now, but it is not necessary. 

A box may be made to hold the blueprint roll so it may 
be pulled out and torn off in a lighted room. 

Large printing frames to roll out of a window on tracks 
are used in some drawing rooms. Automatic electric printers 
and washers are available for the blueprinting concern or 
the big plant. 




90 


Mechanical Drawing 


Assignments: Make a blueprint from one of the tracings 
made under instructions contained in Chapter XVIII. 


CHAPTER XX 


The 10 x 14 Standard Sheet 

All of the drawing problems following this chapter are to 
be drawn on a new sheet size. The sheet used so far was 
9x12, with a half inch border and a minimum of lettering. 
The new sheet Has 10"xl4"~drawing space, 1" at bottom for 
lettering, 1" at left for border, and border at top, bot¬ 
tom, and right. This sheet was inspired by a drawing ap¬ 
pearing in a recent number of the “House and Garden” Mag¬ 
azine. The drawing is reproduced in Figure 75. 



gested the standard sheet form used in this text. 

Detailed dimensions of this sheet are found in Plate XVI, 
which gives a letter sheet designed for this size of sheet. 


[91] 









































92 


Mechanical Drawing 


Note that all lettering in the center space at the bottom is 
upper case, and that all lettering in the two end spaces is low¬ 
er case. 

Note: Assignments given hereafter, require a complete 
and finished drawing, fully inked, and every third sheet must 
be dimensioned. 

Assignment: Lay out four sheets of the new size; let- 
tem completely, except for name of drawing. Drawing No. 19. 
On the first sheet make a new letter sheet exactly as laid out 
in Plate XVI. 


Mechanical Drawing 


93 



Place XVI. The 10x14 standard sheet. 


















































































































































































































CHAPTER XXI 


Sectional Views in Mechanical Drawings 

When the inner details of an object cannot be clearly 
shown by representing the hidden or invisible lines with dot¬ 
ted lines, a part of the object is imagined as cut away to ex¬ 
pose the inner details. This is called making a sectional view. 
The full section, showing an object cut in halves with all of 
the inside lines becoming visible is exemplified in Figure 76. 



Fig. 76. Full sectional views of a ball-bearing loose pulley and an emery 

wheel. 

When an object is cut entirely through the center, the 
resultant drawing is called a full sectional view. The section¬ 
ing of objects is usually accomplished by passing a plane 
through the center-line. Actual problems showing sectional 
views are often made for the drawing room by sawing a model 
into two equal parts with a hack saw. Cross section lines are 
used to represent the surfaces sawed apart, and they actually 
may represent the saw marks. The following general rules 
govern making sectional views: 

1. The shaft in the center is not cut, and is therefore 
not cross-hatched. (Figure 76) 


[941 




























Mechanical Drawing 


95 


2. Do not draw any invisible lines behind sectional 
views. Only details in the plane of intersection are represent¬ 
ed in this view. 

3. Usually only one view is sectional. (Figures 78 and 
79) In any case, the other view does not show the detail of 
sectioning. 

4. Cross-hatch lines to represent different metals are 
made in different ways. (Figure 77) 



Cast 


Iron 



Sloe I 



Brass 



Wrought Iron 



Bobbitt 



Glass 



Rubber 



Concrete 



Face one/ enct grair 
of l^Vooct 


Fig. 77. Standard cross-hatch lines for nine common metals and materials. 

5. Almost all cross-hatch lines are made at 45° to the 
horizontal. Some draftsmen make the lines representing 
steel 60° to horizontal. 





















96 


Mechanical Drawing 


6. Cross-hatch lines run at opposite angles in adjacent 
parts. 

7. Cross-hatch lines run the same direction in all places 
representing the same part. 

When one-fourth of an object is cut away, exposing one- 
half of it for a sectional view, it is called a half-sectional 
view. This is used where the object is symmetrical and the 
full-sectional view would show no additional detail. The pur¬ 
pose of the half-sectional view is twofold; first, to save the 
time required to 1 draw and ink the detail required in the full- 
sectional view; second, to show in half of the drawing all of 
the lines representing the outside of the object and at the 
same time all of the inner details in the other or sectioned half 
of the drawing. 



In Figure 78 is shown a half-sectional view of a babbitted 
sleeve for a clutch. Each sleeve has a 5/16" shell of babbitt 
in it. The sizes of three of these clutches are given in the 
following table: 


Dimensions 


For 

all 

clutches 

II II 1 1 1 1 

| B | C |D | E |F|H| K I 

Pulley 

Face 

G 

1 Shaft 

| Size 

10" 

to 

14" inclusive 

| 2 %| 8%I6 | 7 iy 2 iviH 1 

6" 

14% 

1 2% 

16" 

to 

24" inclusive 

13 |11%!8 T 9 E |10 \%wv.uw 

6" 

15 

1 3 

28" 

to 

30" inclusive 

3% 13%|9 |ll%|%|%|l%| 

6" 

15% 

1 3% 


When only a part of an object is cut away to show an in¬ 
ner detailj the drawing is called a partial-section. Frequent- 

































97 


Mechanical Drawing 


1> an object is symmetrical about an axis and also of the same 
size and material throughout its length. In this case much 
time and work can be saved by half-sectioning a part of the 
length. In Figure 79, the object is clearly shown by the 



Fig. 79. A partial section of a babbitt-lined sleeve. 


partial section at left of front view. Partial sections may be 
used at any place in a drawing, or even in several places in 
the same drawing. Figure 80 shows four partial sections in 
the same drawing. 



Fig. 80. Using partial sections Gf parts in an assembly drawing. From the 
South Bend Lathe Book. 

Cross hatching lines are usually drawn without mechani¬ 
cal aid for spacing them. For ordinary work, this is the usual 














































98 


Mechanical Drawing 


way, but in special work on show drawings, a section liner is 
used. Figure 81 shows a rather practical form of mechanical 
spacer for drawing cross-section 1 nes. 



Fig. 81. A cross-iseetion liner. 


Drawing No. 20. Draw top and front views and make 
full section front view of any size lever end given in Figure 
82, using the table of sizes given below: 



Fig. 82. A standard lever end. 


Table of Sizes of Lever End 


A 

1 B 

1 c 

1 D 

E 

1 F | 

H | 

K I 

L 

I M , 

| liOlfr 

1* 

in 

2 ft 

2ft 

3 

3% 

4 

5 

9 y 2 

ioy 2 

8% 

10 

3'% 

3% 

sy 2 
3y 2 1 

I 2% 

j 2 
! 2% 

2ft 

3ft 

2ft 

2ft 

y 2 

y 4 

% 

% 

1 1 

1 

% 1 

1 3 ‘ 

! 4 

I 2% 

1 3 

1 1% 

i iy 2 

i i% 

1 1% 

| % 

I % 

1 % 
% 

2 Hr 

5V 2 

11 

4% 1 

21/4 

3ft 

:i / 2 

1% 

3 

i i% 

*4 


Drawing No. 21. Make half section front view of flanged 
bearing described in Figure 83. This bearing has a lining of 
of babbitt next to the shaft. Use the dimensions given in 
the table below and in the larger sizes, draw a half circle for 
right end view. 






























Mechanical Drawing 


99 


Table of Sizes of Flanged Bearing. 


Shaft 

Sizes 

A 

B 

1 T 

D 

E 

F 

0 

Bolts 

m 

5% 

3% 

I % 

2 Vs 

5 t /8 

% 

4 % 

4V 2 

It* 

6 

41/4 

1 u 

3'4 

6 V 2 

% 

5 

4V 2 

2 A 

6 % 

4% 

1 % 

3% 

7% 

% 

5V2 

4% 



Fig. 83. Flanged bearing-—babbitted. 


Drawing No. 22. Make a full section of the Economy 
center point for lathe tail stock shown in Figure 84. The 
removable point is high speed steel; the other parts are m Id 
steel. Draw front and right views. 



Drawing No. 22a. Make a two-view drawing of one of 
the babbitted sleeves in Figure 78. 



> » 
> > i 












































































CHAPTER XXII 


Tangent Problems 

Tangent problems are very common in, mechanical draw¬ 
ing. The ability to recognize them and to understand the 
geometry governing them will aid greatly the draftsman who 
hopes to progress satisfactorily. The experienced draftsman 
may locate centers of circles and points of tangency by guess, 
but he understands quite well where these are and aided by a 
clear conception of final appearances, he can guess to an ac¬ 
ceptable degree of accuracy. But the beginner, in represent¬ 
ing a rounded corner, might miss the required quarter circle 
by as much as ten degrees. 

The general consideration of tangents has been divided 
into five groups based on five common tangent problems. 
These five cases of tangents are similar to as many theorems 
in geometry. At least two drawings should be made involving 
each of these cases of tangents and in each advanced prob¬ 
lem, the cases already covered will possibly be included. 

Five Cases of Tangents. 

Case I. When a circle.is tangent to two perpendicular lines. 
Case II. When a circle is tangent to two parallel lines. 

Case III. When a circle is tangent to two divergent lines. 

Case IV. When a circle is tangent to a line and a circle. 

Case V. When a circle is tangent to .two other circles. 

Two general problems are always necessarily considered 
in these tangent cases. First, having given the lines to which 
the circle is tangent, the center of the tangent circle must be 
located. Second, after the tangent circle is drawn, the points 
of tangency must be located. These problems involve a very 
delightful application of the geometry of the locus of points. 


CHAPTER XXIII 


Tangent Problems Case I 

Wh en a circle is tangent to two perpendicular lines. 
Many manufactured articles are improved in appearance and 
usefulness by being made with rounded corners. This is par¬ 
ticularly true of comers of castings. Fillets in castings, or 
inside round corners are also typical of this case of tangents. 



Thet cast iron tool rack shown in Figure 85 is a good ex¬ 
ample of the common use of rounded corners. This drawing 
shows the pencil drawing of the three views of the tool rack. 
After the three views are blocked out, the circle is drawn in 
the top view and the throat is drawn and projected to the 
front view, we have the problem of drawing the tangents. 

The center of the tangent circle is located as follows: 

Set compass at desired radius. With corner as a center 
“c”, (Figure 85) draw short arcs on the two lines, a and b; 


[101] 














102 


Mechanical Drawing 


with a and b as centers draw two arcs intersecting at “d”. 
This will be the center of a circle tangent to the two perpen¬ 
dicular lines. Other methods may be used providing always 
that the solution may be proved by geometry. 



Fig 86. Photograph of easy tangent problem. 


The points of tangency will he at the intersections of the 
first arcs and the two perpendicular lines, or at a and Jb. In 
inking the drawing, the points of tangency are of great help, 
ink all circles and arcs of circles first. Thus the quarter circle 
a-b will be inked. Then, after arcs of circles, all straight lines 
are inked. The line b-x is inked from the point of tangency 
b to the comer x. The line a-y is inked later, from the point 
of tangency, a, or the end of the quarter circle to the point of 
tangency, y. Good joints must be made when inking. The 
ruling pen must be set to draw a line of exactly the same 
thickness as the inking compass draws. 

Be sure to follow the order of inking as suggested above, 
and as was given in Chapter XIV for all tangent drawings. 

Drawing No. 22. Draw three views of any problem given 
in figures 86 or 87. 









Mechanical Drawing 


103 


Drawing No. 23. Draw two or three views of any one of 
the problems given in Plate XVII. 



Fl'\ 57 . rtotcgraph of easy tangent problem. 









104 


Mechanical Drawing 



Plate XVII. Tangent Problem Case 














































































































CHAPTER XXIV 


Tangent Problems, Case II 

When a circle is tangent to two parallel lines. Rounded 
ends »of castings, slots with rounded ends, and chain links are 
typical of this case of tangents. This problem occurs very 
frequently in machine drawing. 



Fig. 88. The front view of a rocker arm showing examples of Case II of 

tangents. 

The front view of a rocker arm in Figure 88,, shows typi¬ 
cal examples of Case II of tangent problems. There are two 
possibilities for beginning the problem. In the vertical arm 
drawing, it is assumed that the three outline lines are drawn; 
the horizontal arm represents the example of when center 
lines locate the centers of circles. 

When outlining lines are already drawn, the center of the 
circlet.'tangent to the three lines is located by drawing the two 


[1051 




















106 


Mechanical Drawing 




Fig. 90. Tangent problems Case II. 


45° lines from the corners; x-c and y-c in Figure 88. The in 
tersection of these two lines locates the center of the tangent 
circle. 


Fig. 89. Chain links form Case II of tangents. 

The points of tangency are located by drawing a diameter 
perpendicular to the two parallel lines. The line p-p in Fig¬ 
ure 88 locates the two points of tangency. These points of 
tangency locate the exact places where the circle stops and 
lines begin. 

When center lines locate the centers of the half circles, 
draw the circles first and then draw the lines tangent to the 
edge of the circles. The center lines through points m and n, 
Figure 88, locate the centers of the circles. Draw a little 
more than half of the circumference of the circles with the 






Mechanical Drawing 


107 




pencil compass; then draw the horizontal lines tangent to 
these circles. 

Center lines locating centers of circles, when extended, 
locate points of tangency. The six points p' are the points 
of tangency as located by the center lines, extended. When 
inking the drawing, ink all half circles first, then ink straight 
lines joining them,. 


Fig. 90a. Tangent Problem Case II. 

Drawing No. 21. Draw three views of two adjacent 
links of a chain. Each link made of round iron, link 5" 
long, 3" wide. (See Figure 89 J 

Drawing problem No. 25. Draw two views of one of the 
problems in Figure 90, Figure 90a or Figure 91. 


Fig. 91. Tangent problems Case II. 











CHAPTER XXV 


Tangent Problems, Case III 

When a circle is tangent to two divergent lines. The pack¬ 
ing gland is an excellent example of this tangent problem. 
Figure 92 shows two views of a packing gland. In the front 
view, the problem of a circle tangent to two divergent lines 



Fig. 92. A packing gland, showing all of the circles and one line already 

inked. 

is well illustrated. There are two divisions of this problem. 
First, when the circles are already drawn and the straight 
lines are drawn tangent to the two circles; second, when the 


[10S] 










































Mechanical, Drawing 


109 


lines are given and the circle of given radius must be drawn 
tangent to both of them. 

In Figure 92, the center lines a, b, d and e are first lo¬ 
cated and drawn. Then all of the circles with centers at c, c, 
and c, are drawn. The circles o, m, and n, should be drawn 
in their entirety. The four tangent lines, x-y are then drawn, 
just touching the circles. The problem now is to locate the 
points of tangency at x and y. 

The point where a line is tangent to a circle may he lo¬ 
cated hy drawing a line through the center of the circle, per¬ 
pendicular to the tangent line. To locate the points of tan¬ 
gency x or y in Figure 92, it is only necessary to draw a line 
c-x/ or c-y, through the center c, perpendicular to the line x-y. 

To draw a line perpendicular to a given line, set the hy- 
pothenuse of either triangle on any straightedge with either 
leg coinciding with the given line; slide the triangle along the 
straightedge until the other leg intersects the line at the prop¬ 
er point. This trick of the trade is well worth knowing. Re¬ 
fer to Figure 93 for a graphic representation of this rule. 
The given line A-B is at an odd angle to the horizontal. The 
45° triangle is placed with the hypothenuse on the tee square 
so that one leg coincides with the line. The triangle is moved 













110 


Mechanical Drawing 


along the tee square until the other leg coincides with the 
point P. The line P. Q. is then drawn perpendicular to A-B. 

Thus, the, points of tangency x and y are located and the 
circles are inked only to these points. The straight lines join¬ 
ing these arcs of circles are then inked. 



Fig. 94. Locating the center of a circle tangent to two given divergent lines. 

When two divergent lines are given, (See Figure 94), the 
center of the circle tangent to them both is solved as follows: 



Fig. 95. The locus of centers of circles tangent to a line. 




Mechanical Drawing 


111 


The locus of the center of a circle of given radius tangent 
to a line is a line parallel to the given line and one radius dis¬ 
tant on either side. Figure 95 shows a line parallel to the 
given line, Ai-B in which centers of all circles on top of this 




' * 


Fig. 97. A rocker arm and a packing gland Involving Case III of tangents. 





















112 


Mechanical Drawing 


line tangent to the given line are located. Thus, in figure 94, 
with the two lines A-B and C-D given, step off from each line 
with the dividers the distances “R. ” Through the points 
thus located, draw lines x-y and m-n (See Figure 96) paralled 
to A-B and C-D respectively; where these lines intersect is 
the center of the one circle tangent to both lines. 

This requires a knowledge of another “trick of the 
trade” of mechanical drawing. To draw a line parallel to a 
given line, set either triangle on any straightedge so that 
any side of the friangle coincides with the line; slide the 
triangle on the straightedge and any line drawn on the sayne 
edge will he parallel with the given line. (See Figure 96.) 

This case of tangents is very common. Too frequently 
all of the work of locating centers of circles and tangent 
points is done by guess. This is often an admission on the 
part of the draftsman of a lack of knowledge of geometry, and 
of a careless nature. 

Drawing No. 26. Draw two view T s of the packing gland 
or rocker arm, Figure 97. 

Drawing No. 27. Draw two views of either problem 
shown in Figure 98. 



Fig. 98. A flask weight and a web for a reel. 






CHAPTER XXVI 


Tangent. Problems, Case IV 

When a circle is tangent to a line and another circle. 
This case is shown in Figure 99. This figure shows the line 



A-B and the circle with center at C. The smaller circle, BF, 
with its center at, 0 is tangent to the line and the circle. 

The locus of the center of circles tangent to a given circle 
is another circle with the same center and radius equal to 



the sum of the radii of both circles. Figure 100 shows a con¬ 
centric circle outside the given 
circle, With the same center, which 
contains the centers of all circles 
of the given radius which mil be 
tangent to the given circle. Thus 
the intersection of the line, D 0 in 
Figure 99 with the circle, B 0 E, 
will be the center of the one circle 
tangent to both the line A B and 
the circle whose center is at C. 
The distance from A-B to the line 
D 0 and from the given circle to 

Fig. 100. The locus Of the cen- the outer circle should be stepped 
ter of circles tangent to a circle, off with the dividers. 

[113] 




114 


Mechanical Drawing 


When two circles are tangent, the point of tangency is 

located by joining the two 
centers with a straight line. 
This is shown in Figure 
101. So in Figure 99 join 
the centers 0 and C to lo¬ 
cate the point of tangency, 
F. When inking, draw the 
circles first and then draw 
the lines joining the c : rcles. 

Handwheels and pulleys 
form a splendid example of 
this case of tangents. Hand 
wheels apply all of the tangent problems so far considered. 



Fig. 101. When two circles are tangent, 
draw a line of centers ;o Locate the point of 
tangency. 



In Figure 102 the sectional view cuts through a spoke 
and the spoke is sectioned. The conventional representation 





























115 


Mechanical Drawing 

of wheels is shown in .Figure 103 in which the spoke is not 
sectioned. This method is used even when the spoke ap¬ 
parently should be sectioned. 



Fig. 103. Handwheels and pulley sections do not always cut spokes. Time 
m drawing crossrhatch lines is thus saved. 

Drawing No. 28. Draw three views of either problem in 
Figurei 104 or Figure 104a. 

Drawing No. 29. Draw full front view and full section 
of right view of any handwheel given in table below. 
Handwheel rim is round and there may be four or six spokes. 
(See Figure 102) Draw half of face view in large sizes. 



Fig. 104. Two floor clamps applying Case IV of tangents. 














































116 


Mechanical Drawing 



Fig. 104a. A rocker arm and a wrench. 


Table of Sizes of Handwheels 


Diameter 
of wheel 

1 Spoke | 

1 at rim 

1 

i i 

Spoke 
at Hub | 

Diameter | 
of Hub | 

Diameter | 
of rim | 

Diameter | 

of round 
hole in | 
Hub 

Thickness 

of Hub 

6 

1 I 5 5 x% 

%x % 

i* 

it 

i 9 s 

Itk 

7 

1 i\x% 

%x % 

i% 

1 

11 

iy 2 

8 

| %X% 

%Xl" 

1% 

l A 

Vs 

2 

9 

1 MX}* 

%xiy 8 

1% 

i% 

1 

2% 

10 

1 

Hxl% 

l 3 4 

1t% 

1 

2% 







































CHAPTER XXVII 


Tangent Peoblems, Case V 

When a circle is tangent to two other circles. This prob¬ 
lem may occur having either the two circles or the tangent 
circle given. The contrast is represented in Plates XVIII 
and XIX. The solution of the second problem on Plate XVTII 
is shown in Figure 105. The two circles with centers at C 
and C and the one with the center at 0 are given. The 
problem is to locate the center of a circle with radius R which 
will be tangent to the C circle and the 0 circle. Set the di¬ 
viders at a distance R and step off outside the 0 circle on 
a radius extended, 0 M, the distance R. This distance is 
stepped off three times, once on each circle. It must be 
measured on a radius extended because otherwise it would 
not be accurate. 



With compass set at centers C, C and 0, draw arcs of 
circles P X, Y Q, X N and M Y through the points located 
with divider. The intersections Xand Y will be centers of 


[ 117 ] 
















Plate XVIII. Tangent Problems ('ase V. 

































Mechanical Drawing 


119 


the only circles of the given radius which will be tangent to 
both circles. 

To locate the points of tangency, draw the line of cen¬ 
ters, X C, Y C, X 0 and Y 0. In inking this problem, 
first ink the circle with center at 0, then ink circles with 
centers at X and Y, inking from the ends of arcs previously 
drawn. Then ink circles with centers at C and C, inking from 
end of arcs already completed. Lastly, ink the horizontal 
lines joining the bottom of circles whose centers are C and C. 

For correct use of the dividers in laying out lengths, 
refer to Chapter XXIX on Thread Drawing. The use of 
compasses and dividers invites a very wrong practice, that 
of punching large and unsightly holes through the ! paper. 
This should be avoided as much as possible; very small holes 
will be covered by the inked lines, but large holes punched 
through the paper are inexcusable. This is particularly true 
of centers of tangent circles which are never hidden by in¬ 
tersecting center lines, but are out in the open spaces of the 
sheet. 

Drawing No. 30. Draw three views of either problem 
given in Plate XVIII. Dimension the drawing and make a 
tracing. 

Drawing No. 31. Reproduce on a regular sheet, either 
problem given in Plate XIX. Dimension the drawing. 



TIGHTENER FOR CRAIN 



SWING TYPE OF CHAIN TIGHTENER 


Plate XIX. Tangent Problems Case V. 






















































CHAPTER XXVIII 


The Helix 

A helix is the path which a point makes on a cylinder 
when the cylinder is revolving at a uniform rate of speed 
and the point moves parallel to the axis of the cylinder at a 
uniform rate of speed. When the machinist begins to cut 
a thread on a bar of iron 2*4'** in diameter, he sets the gears 
of the lathe so that for every full revolution of the cylinder, 
the point of the .thread-cutting tool moves along parallel to 
the axis just y 4 ". The point of the tool traces a true helix on 
the face of the cylinder. 



Fig. 106. A helix of two revolutions. 

In Figure 106 we see the front and right views of a 
cylinder. Al helix having a pitch of 2" has been drawn. The 
pitch of a helix is the distance it advances along the cylinder 
in one revolution. The first one-half revolution 1-13 is visible 
and is plotted by dividing the end view circle into'twenty-four 
parts. (See Figure 171, Chapter XLVI). The pitch f of the 
helix is also divided into twenty-four parts or the first half 
revolution is divided into twelve parts. The helix starting 
at the point 1, advances 1/12" when it is even with point 2 in 
the right view. Thus, the points 1, 2, 3, etc. are plotted. After 
the points are located, the curve is drawn with a curve called 


[121] 





































122 


Mechanical Drawing 


a French or irregular curve. This helix is symmetrical so 
that when a place on the irregular curve is found to fit one 



Fig. 107. French or irregular curves. 


end, mark it with a pencil, and use the same part of the ir¬ 
regular curve on the other end of the helix. 

When one-half of a complete revolution of the helix is 
plotted and drawn, a templet is made so ’that the other parts 
of the helix may be drawn exactly the same and without the 
necessity of'plotting each of them. The templet is made of 
very thin, soft wood and should be made by placing the wood 
over the drawing and after 'drawing lines 1-1, 2-2, 3-3, etc. 
in Figure 106, step off from the points 1, 2, 3, etc. an 'equal 
space, using ,the dividers, on to the wood. Then the curve 
may lie drawn through these points. By using the templet 



Fig. 108. Templet made of 1/16" wood stock for a helix in figure 106. 

the remaining portions of 'the helix may be drawn. Each 
alternate half of the helix will be invisible and should there¬ 
fore be represented by 'dotted lines. 

The helix is a very common curve in machine parts and 
tools. Helical springs or 'coil springs typify a practical use 









Mechanical Drawing 


123 


of the helical curve. Auger bits and drill bits show helices 
in each face view. Conveyors are another type of use of the 
helix. 





Fig. 109. Auger bits and twist drills show the helix and its application. 

All screw threads are helical in their real'representation. 
The face view of every thread will show curved lines for the 
root or point lines of the thread. Figure 110 shows an actiual 
photograph of a large thread on the drive shaft of a Ford- 
son Tractor, in which the curve of the root and point lines 
is apparent, so that an actual and true representation of these 







124 


Mechanical Drawing 


threads would require that the helix for the point line'and 
the helix for the root line be plotted. 'Yet in most actual rep¬ 
resentation these lines are drawn as straight lines. 

Drawing No. '32. Draw two views of a cylinder 4 y 2 " 
in diameter and 8" long, and draw three revolutions of a helix 
having a pitch of 2V 2 ". 


CHAPTER XXIX 


“V” Threads 

There are two common forms of the “V” threads, the 
sharp “V” and the U. 'S. Standard. The first is the theoreti¬ 
cal shape and forms the basis for representing all “V” 
threads. The second is 1 the practical thread found on all 
bolts and in all nuts using “V” threads. 

Pitch is the distance from the center of one thread to 
the center of the next. This is true for single, double, or 
multiple threaded parts. The lead of a screw is the distance 
the nut will move when turned a full revolution. Pitch and 
lead are equal for single-threaded screws. The lead ' is twice 
as great as the pitch in a double-threaded screw, etc. The 
number of threads per inch equals one divided by the 



[125] 




















126 


Mechanical Drawing 


pitch. Thus on a 1" bolt the threads are 1/8" apart, so there 
are eight threads per inch. 

The sharp “V” thread is made with the point and root 
an acute angle, each being 60°. (Figure 111) For various 
standards of threads, all bolts of the same size have the same 
number of threads per inch. 

The U. S. Standard Thread is similar to the sharp “\ ’ 
except that the tops or points and the roots are flattened to 
1/8 the entire depth of the thread. (Figure 112) This makes 
the cutting of the thread easier. The thread-cutting tool does 
not become dull so easily. It also does not interfere with 
the strength of the bolt land thread. 



The' following order should be followed when drawing the 
“V” thread (See Figure 113.) 

a. Lay off number of points per inch on one side of 
rectangle representing side)view of cylinder. 

b. Use 60° triangle and draw one side of sharp Ys. 

c. Draw other side of Vs. ; 

d. Project from roots of these Vs to' get points on other 
side of rectangle. 

e. Draw Ys on other side of rectangle. 

f. Draw all lines of points, sliding triangle on tee square 
to draw them parallel. 

g. Draw all lines of roots same way. Root lines are 
not parallel to point lines. 







Mechanical Drawing 


127 


h. Project root bottom to end view and draw doited cir¬ 
cle representing bottom of thread. 


VvVWVI 


Jb c 


VVVYYV1 


WWW 
/WWY 

e. 

Fig. 113. Method of drawing “V” threads. 



When laying off points of the threads, if the pitch equals 
Vs, 14 , Ys, 1/16, 1/12 part of an inch, or when the pitch is 
found on the scale, use the scale for locating points. Thus, on 
the 2 y 2 " bolt there are four threads per inch. Lay off 'the 
points 14" apart. When there is an odd number of threads 
per inch such as 5, 7, 9, 11, etc. use the dividers for locating 
the points. First lay off each inch point on one edge of 
the cylinder. Then on the waste edge of the sheet, lay off 





Fig. 114. The dividers, plain and hairspring types. 


one inch and set; dividers so they will step off the required 
distance. Step this off on the sheet, being careful not to 
punch holes through the 1 paper. Punch small holes, holding 



































128 


Mechanical Drawing 


the dividers at an angle of 15° to 30°, to surface of paper; the 
pencil lines will then cover holes. Dividers,are so called be¬ 
cause of their use; to divide an inch into 3, 7, 9 parts, etc. 
When there are 3y 2 threads per inch, divide a 2" length into 
7 parts and lay off points. 

After the points are jlaid out, the sides are drawn and 
the points on the opposite side are found. In a single p tch 
thread, roots are opposite points and points are opposite 
roots., To sketch a “V” thread draw two rail fences with 
each opposite rail parallel. (See a, Figure 115.) Keep 



Fig. 115. Sketching a single-thread sharp “V” screw. 


points opposite roots and roots opposite points. After the 
two sides are drawn, join, all points, then join roots. Notice 
that root lines land point lines (See b, Figure 115) are not 
parallel. These are never parallel and should not be so 
drawn. 



Fig. 116. Stud bol'.s. 


Sharp “V” threads appear best when the outl’ne of 
threads and point and i root lines are drawn. Several con¬ 
ventional methods of representing them are permissible. In 










Mechanical Drawing 


129 


Plate XX the top screw shows threads in profile while the 
stove-bolt in the bottom of the bowl shows a conventional rep¬ 
resentation,'of sharp V threads. Figure 76 shows the threads 
on the grinder shaft in a conventional representation. 

One of the simplest thread drawing problems is the Stud 
Bolt shown in Figure 116. These bolts are threaded on each 
end with U. S. Standard threads a distance of 1/3 of the 
length. 

Drawing No. 33. Draw two views each of two stud bolts: 
one 1 x9 , U. |S. Standard e : ght threads per inch; the other 
2y 2 x9" U. S. Standard with two threads per inch. The first 
is a standard thread;’the second is too large for the bolt but 
shows better that root lines and point lines are not parellel. 

Drawing No. 34. Draw helical representation of sharp 
V threads on,a 5 y 2 " bolt 9" long. Draw a half circle represent¬ 
ing end view and draw five full threads having a 'pitch of 
1 y%". (Similar to Figure 123) 


•/k/T-ftAcm- 


130 


Mechanical Drawing 



July !6,1924 _ OKLAHOMA A6M COLLEGE _ 

Plate XX. Nut bowl and nut cracker showing thread drawings 
















































































CHAPTER XXX 


Bolts and Nuts 

There are so many kinds of bolts and nuts that it would 
require many pages to list and illustrate them. Complete 
details of the commoner types may be found in such reference 
books as “Machinery’s Hand-book.” Several kinds, such as 
Machined bolts, Carriage bolts, and Automobile holts are 
common enough to learn to draw. All are drawn in similar 
ways. The U. S. Standard Machine bolt, which will be de¬ 
scribed, is typical of all of them. 

The sizes of the U. S. Machine bolt are given for different 
diameters as follows: 

Table of Sizes of U. S. Standard Machine Bolt 

Square or Hexagonal Heads and Nuts_ 


Diameter | No. Threads | Distance | Thickness | Thickness 
j| across flats | of head | of Nut 


1% 

1 

6 

2% 

1* 

iy 2 

1% 


5 

2% 

1% 

i% 

1% 


5 

21-J 

1H 

i% 

2 

1 

4% | 

3% 

i& 

2 

214 

I 

iy 2 

1 3% 

l% 

214 

2V 2 

1 

4 

3% 

ill 

2% 

3 


3y 2 

4% 

2fy 

3 


From this table the bolt may be drawn, following Plate 
XXII for methods of representing the chamfer on the nut 
and head, and for rounding end of bolt. 

The number of threads per inch varies for different k'nds 
of threads. The table in Figure 117, shows U. S. Standard, 


Stand of d 
of ■/■/tread 

D tosne/ef-s of sereins. 


Si 
3i t 

iqf 

,1* 

z. 

% 

* 

.2. 

% 

JL 

SL 

7? 


7- 

r 



'i 

// 

it 

z 

zi 

1L 

a 

3 

US Standard 

3C 

m 

21 

20 

It 

ic 

14 

n 

tz 

// 

// 

/O 

9 

r 

7 

7 

6 

6 

s 

4i 

4{ 

4 

4 


>SAE 




ZJ 

id 

24 

16 

Zo 

IT 

/t 

/(, 

/<, 

/4 

/*■ 

/z 

1Z 

tz 

/z 








zt 

24 

zz 

/s 

/! 

16 



















-S mnt/ 

/) c/w# - 


/d. 

1 <s 


yf/V 



Fig. 117. A table comparing the number of threads per inch for different 

standards. 


[ 131 ] 















































132 


Mechanical Drawing 


A. S. M. E. or S. A,. E. (Society of Automotive Engineers) 
Stove bolt, Square and Acme thread standards. This explains 
why a 1/4" nurt of the ordinary variety will not tit on a 14 " 
stove bolt. 

When drawing threads the slope of point and root 1 nes 
indicates right or left hand threads. If the nut is advanced 
on the bolt when it is turned to the right or clockwise, when 
the individual is facing the end of the bolt, the thread is 
right hand. If the reverse is true, the thread is left hand. 
Figure 118 shows sketches of a fright hand and a left hand 
thread. The only difference is in the slope of the point and 
root lines. One use ,of left hand threads 'is on the left end 
of a grinder. When the grinding wheel turns -over and To¬ 



ward the operator, the left hand threads tend to tighten the 
nut holding the wheel. Other uses are on the right hand 
wheels of a wagon, the’adjusting thumb screw of a jack plane, 
etc. The split or sectioned nut in Figure 110 apparently 
shows left hand threads but is in reality the right hand 
threads in section. This is true also of the nut on Plate XXI. 



Fig. 119. A grinder mandrel. 

Drawing No. 35. Draw two views of the grinder mandrel 
shown in Figure 119 with right and left hand threads.' 





















133 


Mechanical Drawing 

' drawing No. 36. Draw two views of a 6" Machine bolt 
and nut of any diameter given in table above. Refer to Plate 
NXI for details. 

Drawing No. 37. Draw two views of six kinds of bolts, 
set screws, cap screws, etc. each %" x 4", spacing the problems 
carefully and securing data as to size, shape of head, etc. from 
a “Hand-book.” (See Figure 120.) 





Fig. 120. Six kinds of machine screws: Set screws; counter-sunk, roundhead 
and fillisrer head machine screw’s, and hexagon and square cap screws. 




134 


Mechanical Drawing 



plate XNI. Detail drawing of a II. S. standard machine hoi '. 







































































































CHAPTER XXXI 


Square Threads 


The square thread is so called because the thread pro¬ 
file is practically square. This type of thread is used on 
jack screws, feed screws on machine lathes, and on machin¬ 
ery where great pressures are exerted. Figure 121 shows 
the detail of the square thread and a conventional representa¬ 
tion nearest to tlio real thread. 



Fig. 121.. The square thread. 


Owing to the difficulty of grinding,tools to cut a square 
thread, a varation of it called the Acme Standard has been 
developed. The sides slope at 29°; otherwise it is similar to 
the square thread. It is drawn by laying out as for a square 
thread. (See lower edge of Figure 122). By locating the 
center of the sides ofjthe squares and drawing 15° slope lines 
Through these points, the thread is completed. All root cor¬ 
ner l ; nes are drawn parallel and all point corner lines are 
also parallel. 


[ 135 ] 









136 


Mechanical Drawing 



The square thread affords a delightful application of 
helical representation. Figure 123 shows the actual and 
exact representation of all helices in the square thread. There 
being four helices, two for point lines and two for root lines, 
different templets must be made for the drawing. 























































Mechanical Drawing 


137 


Drawing No. 38. Draw a true representation of four 
turns of a square thread having a)pitch of iy 2 " on a 5i/ 2 " bolt 

9" long. Make drawing 
similar to Figure 123. 
Drawing No. 39. 
>* Draw two views of 
screw and two views of 
nut (one full sectioned) 
shown in Figure 124. 
Pht both drawings on 
one sheet and represent 
Fig. 124. A screw for an adjustable stool, threads as shown in 

Figure 121. Pitch=%". 

The screw is 10" long. 

Drawing No. 40. Draw two views of the screw in Fig¬ 
ure 124, with Acme Standard thread instead of square 
threads. Make the screw 2 y 2 " in diameter and the pitch 




CHAPTER XXXII 


Double-Triple-Multiple-Threaded Screws 

Threads are often made so that in one revolution the 
nut will advance twice, three times, or four times the amount 
of the pitch. This is accomplished by actually cutting two, 
three, or four threads on the bolt. Double-pitch, triple-pitch, 
etc. are not correct terms, since the pitch be ng the distance 
from one thread to another does not change when the lead 
is doubled or tripled. Double-threaded screws are used in 
vises. The Bendix drive uses a triple-threaded screw. 



Fig. 125. The Bendix drive showing a use of a triple-threaded screw. 

When drawing a double-threaded sharp “V” screw, the 
Vs on each side are made so that points are, opposite points 
and roots are opposite roots. Figure 126 shows two steps 
in sketching the double-threaded screw. At the left the A s 





Comp/*/<■ **<■''*''- 


Fig. 126. Method of sketching a double-threaded screw. 







Mechanical Drawing 


139 


are drawn with points opposite points. At the right, the 
point lines slope an amount equal to the pitch in one half 
revolution of the screw. 

The double-threaded square thread screw affords good 
practice in thread drawing. Figure 127 shows a good 
type of representation for a double-threaded square thread 
screw. 



Drawing No. 41. Draw the screw for a veneer press, 
Figure 128. It has a double-threaded screw 5/8" pitch. Make 
the drawing full size, shortening the front view to a suitable 
length. (See Figure 129) Length = 22". 


M 



Fig. 128. A screw for a veneer press. 













CHAPTER XXXIII 


Pipe Threads 

Threads on pipe are always made similar to a sharp V 
or U. S. Standard thread. They taper 1/32' per inch on 
each side of the pipe, so that by screwing the fittings to¬ 
gether, a water tight joint is made. The last three or four 



threads are imperfect, due to the need for short threads on 
the die when starting to cut threads. In drawing the pipe 


STANDARD SIZES 


Nominal Size 

Inside Diam. Outside Diam. 

Threads per Inch 

y 8 

.269 | .405 | 

27 

yr 1 

.364 | .540 

18 

% 

.493 1 .675 

18 

y 2 

.622 1 .840 

14 

% 

.824 1 1.050 

14 

i" 

1.049 1.315 

ii y 2 

i y 4 

1.3£j0 1660 

u% 

i y 2 

1.610 1.900 

ii % 

2" 

2.067 [ 2.375 

u% 

3" 

3.068 | 3.500 

8 

4" 

4.026 | 4.500 

8 


[140] 














































Mechanical Drawing 


141 


threads, after determining the number per inch, draw the 
13^ taper and draw all of the threads as though they were 
perfect. See Figure 129. 

Drawing iso. 42. Draw two views of a piece; of 2 y 2 '' pipe, 
3 long showing threads on each end. Secure dimensions from 
above table. (Shorten front view) 

Drawing No. 43. Draw a full section side and end view 
of a 2 or a 2 1 /?'' globe valve. Borrow one from a plumbing 
shop to get the measurements. 


CHAPTER XXXIV 


House Plans 

A complete set of house plans consists of a plan of each 
lloor, an excavation or footings plan, and a roof plan. In 
addition, there >must be four elevations, showing each side 
of the house with details of door and window anangement 
and wall construction. Then detail drawings must be made 
to show all door and window frame construction, roof fram¬ 
ing, and all built-in woodwork. These are made in plans and 
elevations, the latter often showing sectional views. A per¬ 
spective sketch of the completed building is often made to 
show the owner just what the house will be like. 

The design of a home should include as much built-in 
work as is permissible. Breakfast nooks, closets, seats, book 
cases, kitchen cabinets, etc., if built in, make the house more 
saleable as well as more useful. When planning a home, it is 
well to plan complete plumbing equipment and also complete 
electrical service. Plenty of outlets for electric fans, motors, 
etc. should be provided. Numerous outlets for floor lamps 
and other lights should also be included in the plans. Two or 
three outlets for radio aerials and grounds should be install¬ 
ed, but care must be taken not to parallel electric lines with 
radio circuits. 

There are many conventional methods of representing 
details in house plans. Secure books of details from firms 
specializing in such works 'and adopt a good-appearing type 
of plan and then maintain that style. 

Drawing No. 44. Draw the floor plan of your home. 
Use a scale of 3/8”=T'-0". 

Drawing No. 45. Draw the roof plan of your home. Use 
same Scale. 

The drawing need not be inked; ink the tracing only. 


[142] 


Mechanical Drawing 


143 



SECOND FLOOR 



Fig. 130. A two story brick hous^ showing partial 
arrangement of furniture. Floor plans and per¬ 
spective sketch are shown. 






















































































144 


Mechanical , Drawing 


The first floor plan may be used to assist in making the roof 
pians. 


Legend 

M Master BwitJM' 
D Ceiling Light 
*D Bracket Light 
•43 Base Plug 
>+* Ratio 
-it Telephone 
Switch 
SWayBvitch 
~4 4 Way-Switch 



Fig. 131. A floor plan providing for electrical service, from 
an article by Lee McClure in the “American Builder” for 
April, 1926. (Used by permission). 





































































































Fig. 132. A photograph of the house in Figure 130 after completion. 




















CHAPTER XXXV 


Building Details 

Much detail planning must be done after the general 
floor plans have been decided upon. Sections through founda¬ 
tion, sill, window sill, window head, plate and rafter projec¬ 
tion, must be made. Elevation framing details must be worked 
out. Special problems of framing over wide openings must 
be solved. Rafter plans for roof detail must be made. These 
problems must all receive full attention and must be solved 
in scale drawings before a contractor can make an accurate 
estimate of the cost of the job. 

Details of window and door frames can best (be obtained 
from Millworks catalogs. These are more or less standard 
and should be kept so in the plan. Visit and study houses 
under construction to determine standard practices in com¬ 
mon use. 

Drawing No. 46. Plan and make detail construction 
drawings for a two car garage. Plates XXII and XXIII 
show typical detail plans. 


[1461 


Mechanical Drawing 


147 



Plate XXII. Detail, elevation and framing plans, 




































































































































































































































































































148 


Mechanical Drawing 


Wee* 

MC. ATtttN* 



/!•»*■ »ilw Tl^e*. tint 


Fc.ont Framing Lllvation • 


Section ■ Thuu door* Head 


4* 6TU»» 



*ioo» tint 


Section thu.u Bottom • 6»vl 


• View • Showing 
Fr a me - construction 


Plate XXIII. Section through walls for building details. 





































































































































































































CHAPTER XXXVI 


Building Elevations 

On more complicated jobs, building elevations showing 
each face of the building are necessary. Churches, court¬ 
houses, and other public, buildings; office buildings, apart¬ 
ments, etc. all require complete elevation drawings. Store 
plans are frequently drawn showing only front and rear eleva¬ 
tions, while on buildings with two or more faces, identical, 
one elevation will suffice for all duplicates. 



Fig. 133. Floor plan, roof plan, two sketches, three elevations and a perspec¬ 
tive sketch of a five-room house. (From “The Builder” for March 192(5. 
Used by permission.) 


Drawing No. 47. Plan a four-room ideal bungalow and 
draw three elevations of same. Several sheets may be re¬ 
quired; number extra sheets 47a, 47b, etc. 


[149] 































CHAPTER XXXVII 


Isometric Drawing 


The word “isometric” means equal measure. Isometric 
drawing is a type of pictorial representation based on the 
division of space in a plane by three lines into three equal 
angles of 120° each. The vertical line extends downward 
from the center, and becomes the height axis; one of the 
other lines which is at 30° to the horizontal becomes the 
length axis, and the third becomes the width axis. See Figure 
134. When the true lengths are measured on the length axis, 



Fig. 134. Isometric drawings of a block and of a cylinder. 


the object appears out of proportion. The lines of the ob¬ 
ject are drawn parallel to the axis so that an ,unreal picture 
results in that lines in a picture will not appear parallel. 

The drawing of isometric circles is accomplished as fol¬ 
lows : Draw the three axes as in the right of Figure 134. 
Lay off the diameter OA and OB. Draw AQ and BQ parallel 
to the axes. Draw OX and QN horizontal. Draw QY and 
OM 60° to the horizontal. AB may be drawn. The points 
c and d are the centers of the small arcs XY and MN. The 
points O and Q are the centers of the large arcs XM and YN. 


[150] 







M ECHANICAL DRAWING 


151 


Thus a circle properly foreshortened'is produced. The other 
end of the cylinder is drawn in exactly the same way. The 
sides of the cylin'der are drawn tangent to the circles. 



Fig. 135. Isometric drawings of puzzle joints. 


Isometric drawings are used for pictorial representation 
because of the ease with which they may be made. They are 
sometimes dimensioned and used as working or shop draw¬ 
ings. The lines of the drawing may be shaded and the faces 
colored or tinted, thus producing a very attractive result. 

Drawing No. 48. Draw an isometric projection of any 
of the problems in Plate V. 

Drawing No. 49. Draw an isometric projection of one of 
the cylinders in Plate XT. 















CHAPTER XXXVIII 


Oblique Projection 

In oblique projection one face of the object is drawn 
actual size or in scale, parallel to the 'vertical plane; all depth 
lines are then drawn at 30° or any convenient angle to the 
horizontal. Thus, the true shape of the object 'is seen in 
the face view and its length or width is shown in the oblique 
projection. In Figure 136 the end view of the hexagonal bar 
is drawn and its length is shown by drawing the • side lines 
30 to the horizontal. Frequently the face view in the ob- 



Fig. 136. Oblique projections of a hexagonal bar and a dovetail slide. 


projection is the largest view of the object., (See Plate 
VII). Otherwise, the view which shows the greatest detail 
is drawn in its true shape. (See Plate V) 

The drawing of circles is made very easy, providing all 
circles are parallel to the Vertical Plane. The circles are 
drawn in their true shape instead of being elliptical as in 
isometric drawing. 

Drawing No. AO. Draw the library table in Figure 69 
in oblique projection. Use a convenient scale. 


[152] 













CHAPTER XXXIX 


Orthographic Projection of Lines and Points 

Somei discussion of the basic theory of mechanical draw¬ 
ing was included in Chapter I. The following chapters con¬ 
tain some of the easier abstract problems involving the prin¬ 
ciples of orthographic projection. The complete study of 
these principles constitutes the subject called Descriptive Ge¬ 
ometry. 



Representing a point in the third angle, we use the H 
plane over the point and the V plane in front of the point. 
(ISee Chapter 1.) Thus, the top view of the point is the H 
projection and the front view is the V projection. In the 
drawing, a heavy line is drawn representing the Ground 
Line. All H projections are shown above the Ground Line, 
and all V projections are, shown below the Ground Line. (See 
Figure 137) The following rules apply. 

The H and V projections of a point lie in a line perpen¬ 
dicular to the G. L. 

The H projection is as far above the G. L. as the point 


[153] 








154 


M echanicai, , Drawing 


is bach of V. The V projection is as far below the G. L. as 
the point is below H. If the point is ,in H or V one of its 
projections is in the G. L. With these rules given the follow¬ 
ing problems are to be solved: 

Drawing No. 51. Draw top and front views of a 3, 4, 
6, 8, or 12 sided prism, (See Chapter 46) and locate at right, 
the top and'front views of four points in the drawing. (See 



Fig. 138. Two views of points in a drawing. 

Figure 138.) Space the points about %" apart and also 
draw some of the following problems on the same sheet: 

1. Draw H and Y projections of a point 2” below H and 
2" back of V. 

2. Draw H and V projections of a point 3" below H and 
1" back of Y. 

3. Draw H and Y projections of a point 1" below H and 
3" back of Y. 

4. Draw H and Y projections of a point in H and 3” 
back of V. 



















Mechanical Drawing 


155 


5. Draw H and V projections of a point in H and 2" 
back of V. 

6. Draw H and V projections of a point in the ground 

line. 

7. Draw H and V projections of a point U” below H and 
3" back of V. 

Note. When designating points in the following draw¬ 
ings, use capital letters. For H or V projections use a sub- 
capital letter as shown in Figures 137 and 139. When one 
point in a projection covers another put the lettler designat¬ 
ing the nearest one outside the figure and the letter designat¬ 
ing the hidden point inside the figure. See points 1 and H, 
Figure 140. 


CHAPTER XL 


Projections of Lines 

The direction of a line is located by locating two points 
in the line. So the drawing of lines really consists in locat¬ 
ing the end points. The following rules govern the represen¬ 
tation of lines '■ in orthographic projection: 

1. When a line is perpendicular to either plane, its pro¬ 
jection on that plane is a point.' (See L K, Figure 140.) Its 
projection on the other plane is perpendicular to the G. L. 
and shows the true length of the line. 

2. When the line is parallel to both planes, its projec¬ 
tions are both parallel to the G. L. and both show the true 
length of the line. (Figure 139). 




Fig. 139. Two projections Gf a line in the third angle wi'h the resulting 
drawing of the two views. 


3. When the line is parallel to one plane but at an angle 
to the other, its projection on the one plane shows its true 
length but its projection on the other plane is foreshortened. 
If the line is parallel to the V plane its H projection is par¬ 
allel tot he G. L. See line A H, Figure 140. 

4. When the line is not parallel to either plane, neither 


[156] 

















Mechanical Drawing 


157 


projection is parallel to the G. L. and neither projection 
shows the true length. See B A, Figure 140. 



Drawing No. 52. Draw top and front views of the frus¬ 
tum of a 4, 6, 8, or 12 sided prism of the dimensions given in 
top-left, Plate XXIV and fill almost all of the balance of sheet 
with lines taken from these views. (See Figure 140). Solve 
the problems given below on this sheet. 

1. Draw two views of a line 1" long parallel to H. and 
V, 3" below H and 3" back of V. 

2. Draw two views of a iy 2 line 60° to H, top y 2 " be¬ 
low H and line 2” back of V. Line is parallel to V. 

3. Draw two views of iy 2 " line 45° to V, top %" back 
of V and line 1 y 2 below II. Line is parallel to H. 


































CHAPTER XL I 


True Length of Lines 

When neither view or projection of a line is parallel to 
the ground line , neither view shoivs its true length. (Ex¬ 
ception, when the line itself is perpendicular to one plane). 
This makes it necessary to be able to find the true length of 
the line when the two projections are given. We know that 
when one projection is parallel to the G. L., the other projec¬ 
tion shows the true length. So by revolving either projec¬ 
tion until it is parallel to the ground line, then determining 
what happens to the other, we are able to solve the problem. 
In Figure 141, at left, the two views of the line AB are 




Fig. 141. Two views of a line parallel to neither plane, showing method of 
finding its true length. 

neither one parallel to the G. L. and therefore neither view 
shows its true length. The H projection is revolved on Ah 
as a center until it becomes Ah, B'li, parallel to the G. L. 


[158] 












Mechanical Drawing 


159 


What happens to the V projection ? The point B was moved 
parallel to the H plane when the H projection was revolved. 
Therefore, the V projection of the point B moves to the 
right, parallel to the G. L. even with B'h; so at the right, in 
Figure 141, we find the point B'v. Joining Av with B'v we 
have the true length of this lne. The true length can be 
found by revolving either the H or V projection until it is 
parallel to the G. L. 

Drawing No. 53. Draw 2 views of the oblicpie Frustum 
of a 3, 4, 6, 8, or 12 sided pyramid given in top left of Plate 
XXV and draw top and front views of any five lines (neither 



Fig. 142. A frustum of a pyramid with solution of true length of six lines. 


































CHAPTER XLII 


Developments and Auxiliary Views 

One of the most practical branches of this type of draw¬ 
ing is the development of surfaces. The Sheet Metal worker 
must make a pattern by which to cut the tin for such things 
as buckets, measuring cups, gutters, etc. The lateral sur¬ 
face and ends of regular prisms and cylinders are easy to 
develop. But when the ends are cut off at an angle, it be¬ 
comes necessary to make an auxiliary view of that surface. 
Figure 143 shows the solution of this problem. The auxiliary 





















Mechanical Drawing 


161 


view is obtained by looking perpendicularly down on the sur¬ 
face. The widths are obtained from the top view and the 
lengths from the front. 

In like manner, the cylinder is developed, excepting that 
the circumference may be figured and measured. In Figure 
144 the cylinder is 1% in diameter; its circumference is 
5.49" (See Chapter XLVIII) or approximately 5y 2 ". The 
development is laid out 5%" and this length is divided into 
24 parts corresponding to the 24 parts into which the top 
view is divided. The auxiliary view and the lateral sur¬ 
face are then developed by locating 24 points and drawing 
the curve through them, using the irregular curve. 

Drawing No. 54. Draw two views and auxiliary view 
and develop lateral surface of either prism in Plate XXIV. 

Drawing No. 55. Draw two views and auxiliary view 
and develop lateral surface of either cylinder in Plate XXIV. 

















































162 


Mechanical Drawing 





















































CHAPTER XLJ11 


Pyramids and Cones 


The surfaces of pyramids and cones are developed by 
rolling them about the apex as a center. Thus, the develop¬ 
ment of a cone is a sector of a circle. By figuring the num¬ 
ber of degrees in the sector, it can be laid out with a pro¬ 
tractor. Figure 145 shows rd cone 5” in slant height and 2 %" 
in diameter at the base. A circle AB is drawn with a radius 



Fig. 145. Development of the surface of a cone. 

equal to the slant height, 5 . On this circle the circumference 
of the bottom is rolled out. This is a distance of 23^x3.1416= 
8.63 . (See Chapter 48) Knowing that the large circle has 
a circumference of 10x3.1416 and that the arc of the develop¬ 
ment has/ a length of 8.63, we can find the number of degrees 

in the sector by taking x360°.' This eauals 98.9°. Meas¬ 
ure this off with the protractor. 

Drawing No. 56. Draw top, front and auxiliary views 
and develop surface of either pyramid in Plate XXV. (See 

[103] 




1(54 


Mechanical Drawing 


Plate XXVI) In laying out the development, it is necessary 
in the lower left hand problem to find the true length of the 
slant height line. 



Fig. 146. A celluloid protractor for measuring angles. 

Drawing No. 57. Draw top and front views and develop 
surface of the cone on plate XXV. Refer to Chapter 48 for 
circumference of circles. 









Mechanical Drawing 


165 



Plate XXV. Pyramids and a cone. 

































166 


JV1 ECHANICAL DRAWING 






p late XXVI. Frustum of a pyramid. 























CHAPTER XLIV 


Conic Sections 

V lien a cone is cut by a plane at an angle greater than 
the angle of the axis with the slant height, the resulting 
curve is an ellipse. 

When a cone is cut by a plane parallel with the slant 
height, the resulting curve is a parabola. 

When a cone is cut by a plane which is parallel to the 
axis, the resulting curve is a hyperbola. 

When a cone is cut by a* plane perpendiuclar to the axis, 
the resulting curve is a circle. 

The plotting of these curves and developments is done 
by dividing the top view into twelve or twenty-four equal 
parts and drawing corresponding elements in the front view. 
All lengths may be secured on these elements. (See Plate 
XX Will.) 

Drawing No. 58. Draw complete development including 
auxilliary view of ellipitical section of cone, Plate XXVII. 
(See Plate XXVIII). 

Drawing No. 59. Draw either hyperbola or parabola 
given on Plate XXVII. Draw complete development. 


L1C7I 


168 


Mechanical Drawing 



Plate XXII. Conic sections. 































Mechanical Drawing 


169 




Plate XXVIII. Development of Truncated cone. 


































CHAPTER XLV 


Intersections 

Many problems result from two similar or unlike parts 
intersecting. The funnel shows two cones intersecting; the 
quart measure shows two cones. The three or four part 
elbow shows several frustums of cylinders. A reducing ell 
may show cylinders and cones intersecting. Thus, the prob¬ 
lem of development of surfaces is readily applicable to real 
shop work. 

When geometrical forms intersect, it is usually neces¬ 
sary to first develop the line of intersection; then from that, 
the lengths of the development may be figured. The following 
problems are given without solutions. If help is needed, 
refer to more advanced texts. 


Drawing No. 

60. 

Makes complete drawing 

of 

Problem 

I, Plate XXIX. 
Drawing No. 

61. 

Make 

complete 

drawing 

of 

Problem 

II, Plate XXIX. 
Drawing No. 

62. 

Make 

complete 

drawing 

of 

Problem 

Ill, Plate XXIX. 
Drawing No. 

63. 

Make 

complete 

drawing 

of 

Problem 

IV, Plate XXIX. 
Drawing No. 

64. 

Make 

complete 

drawing- 

of 

Problem 

1, Plate XXX. 
Drawing No. 

65. 

Make 

complete 

drawing 

of 

Problem 

II, Plate XXX. 
Drawing No. 

66. 

Make 

complete 

drawing 

of 

Problem 

Ill, Plate XXX. 
Drawing No. 

67. 

Make 

complete 

drawing 

of 

Problem 


IV, Plate XXX. 


[1701 


Mechanical Drawing 


171 



Plate No. XXIX 












































































































172 


Mechanical Drawing 



Plate No. XXX 


















































CHAPTER XLVI 


Gymnastics of Mechanical Drawing 

The following problems or tricks which may be worked 
out with the triangles and tee square are well worth knowing. 
They might be called “Tricks of the Trade.” The arrows on 
the lines indicate the direction of the drawing of the lines. 
The given line is always labeled A-B. 


A 





A 



Fig. 147. To bisect a vertical or horizontal line using a trianglr 



3 


Fig. 148. To draw an equilateral triangle having base AB giv«n, hori«o*tal 

or vertical. 


[173] 







174 


Mechanical Drawing 




Fig. 149. To draw an equilateral triangle having base AB given at 15, 30, 

45, or 60° to horizontal. 




Fig. 150. To* draw a square having base AB given horizontal, vertical or 15, 

30, 45, 60, 75° to* horizontal. 



Fig. 181. To draw a square having given the diagonal AB, horizontal, verti¬ 
cal, or 15, 30, 45, 60, or 75° to horizontal. 





Mechanical Drawing 


175 



Fig. 153. To draw a hexagon having base AB given either horizontal or 

vertical. (Second method. 1 



Fig. 154. To draw an octagon having a square given. (Use a compass.! 















176 


Mechanical t Drawing 



Fig. 155. To draw a twelve sided figure with base AB given. (Lines are 

apart.) 





Fig. 157. To draw equilateral triangles inside a circle. 












Mechanical Drawing 


177 



Fig-. 158. To draw sq 



aares outside circles. 




Fig. 159. To draw squares inside circles. 




Fig. 160. To draw hexagons outside circles. 


















178 


M EC HAS IGAL , I )RAWING 



Fig. 103. To divide a circle mto 6. S. or 12 equal parts. 

















Mechanical Drawing 


179 



I-'ig. Hi4. T,c> divide a circle into 24 equal parts. (Combine triangles to obtain 

15° angles.) 










ISO 


Mechanical Drawing 



*D- -lo draw a 24 sided figure outside a circle. (Draw every possible 

tangent using both triangles separately and in combination.) 






CHAPTER XLVII 


Drawing Room Equipment 

The drafting room should if possible have north l'ght. 
If a building can be planned to include north wall light and 
light from the north through a saw-toothed roof construction, 
the light will be ideal. Drawing tables should be placed so 
that the greater part of the light comes from the left-front. 
If this is impossible, with the natural lighting of the room, 
an individual electric light should be provided for each desk. 
Light coming from two sides must be at left of and in front 



Pig. 167. An ideal drawing desk for a public school drafting room. 

of the draftsman. This may be injurious to the eyes, but it is 
necessary for good work. Eye shades may be worn if it is 
found advisable. 

Individual storage drawers and drawing boards const'- 
lute the ideal drawing room arrangement. (See Figure 167.) 
The drawings are kept on the board until completed; then 


[181] 





182 


Mechanical Drawing 


they are turned in to the teacher. No drawing paper should 
be rolled. The teacher should keep the sheet paper and is¬ 
sue it as needed, to prevent its being rolled and stored in the 
small tool drawer. 

For the smaller school, a table sim lar to Figure 168 is 
recommended. A separate board is kept on th s table, but at 
the end of each period the student removes his paper and 
stores it together with his other supplies in a portfolio sim¬ 
ilar to that shown in Figure 20. These portfolios may lie kept 
by the instructor in a storage case having one drawer for 
each section or class. 



Fig- 168. A good type of drawing table for Junior High School classes. 

When drawing instruments are furnished, it seems best 
to buy enough moderately priced sets to issue one to each pu- 
p 1, who is charged with it and perhaps makes a deposit guar¬ 
anteeing its safe return. This centralizes the responsibility 
of its loss or damage to the one student. 

The drawing room must be equipped with a blue-print 
frame and a wash basin. Some blackboard space is desirable. 
Also, a bulletin and exhibit space is very desirable. Good 
drawmgs should be exhibited on this space, a very line ex- 




Mechanical Drawing 


183 


ample of a combination of blackboard and bulletin board may 
be seen in the Tulsa, Oklahoma, high school shops. It is 
shown in Figure 169. Many things may be tacked on such a 
bulletin space, such as drawings from catalogs, tables, maps, 
pictures, and other helpful or inspirational material. 


.O-y . 



. ' ■ _ ~ ' • ■ * 

''Exhibit-Space. - V> - 


' 


' rc. 

‘'‘Exhibit - Space. ■■ 


Exhibit Space. ■ 

Corff^rjoor'coreri/y-' - :~ 

B/ach hoard 

• 1 j : ..: 



y \- * Y: .; - - • ; 



F.v* : ' vAy 


SCla/k 



Fig. 169. Blackboard and exhibit board combination in Tulsa. Oklahoma.- 
High School shops. 














chapter xxxxn 


Useful Tables 

Circumference of Circles 

Diameter 
in inches 

Circum- 
| ference, 

| Inches 

1 

1 Diameter 

1 in Inches 

| Circum- 
| ference, 

| Inches 

1V 2 

4.7124 

1 

6% 

21.205 

1% 

5.1051 

1 

6% 

21.598 

1 

5.4978 

1 



1% 

5.8905 

1 

7 

21.991 



1 

7 Vs 

22.383 

2 

6.2832 

1 

7 y 4 

22.776 

2 Vs 

6.6759 

1 

7% 

23.169 

2 % 

7.0686 

1 

7V 2 

23.562 

2% 

7.4613 

1 

7% 

23.951 

214 

7.8540 

1 

7% 

21.347 

2% 

8.2467 

1 

7 Vs 

24.740 

2% 

8.6394 

1 



2% 

9.0321 

1 

8 

25.132 



1 

8 Vs 

25.525 

3 

9.4218 

1 

8 V 4 

25.918 

3 Vs 

9.8175 

1 

8% 

26.310 

3% 

10.210 

1 

sy 2 

26.703 

3% 

10.602 

1 

8% 

27.096 

3V 2 

10.995 


8% 

27.489 

3% 

11.388 

1 

8 Vs 

27.881 

3 % 

11.781 

i 



3% 

12.173 

1 

9 

28.274 



1 

91/s 

28.667 

4 

12.566 

1 

9% 

29.059 

4 Vs - 

12.959 

1 

9% 

29.452 

4% 

13.351 

1 

9% 

29.845 

4% 

13.744 

1 

9% 

30.237 

4V 2 

14.137 

1 

9% 

30.630 

. 4% 

14.529 

1 

9% 

31.023 

4 % 

14.922 

1 



4 % 

15.315 

1 

10 

31.416 



1 

10% 

31.80S 

5 

15.708 

1 

10 y 4 

32.201 

5 Vs 

16.100 

1 

10% 

32.594 

5 % 

16.493 

1 

ioy 2 

32.986 

5% 

- 16.886 

1 

10% 

33.379 

5 Vo 

17.278 

1 

1 

10% 

33.772 

5% 

17.671 


107s 

34.104 

5% 

18.064 

1 



5% 

18.157 

1 

11 

34.558 



1 

11 % 

34.950 



1 

11 % 

35.343 

6 

18.849 

1 

11 % 

35.735 

6 Vs 

19.242 

1 

11 % 

36.128 

6% 

19.635 

i 

11 % 

36.521 

«% 

20.027 

1 

11 % 

36.913 

r »'/ 2 

20.420 

1 

117s 

37.306 

G% 

20.813 

1 




Decimal Equivalents of Fractions 


:k 1 

.03125 

II 

7 1 

a 5 ! 

.21875 

1 

<11 

.40625 

11 

: U 1 

.59375 

11 

2 5 

;U2 

.78125 1 

U ! .96875 

i\r ! 

.0625 

11 

%4 1 

.25 

i 

ft 

.4375 

11 

% 1 

.625 

11 

1 a 
\ <» 

.8125 | 

1" 11.0000 

1fW | 

.09375 

11 

U2 1 

.28125 


u 

.46875 

11 

1 

.65625 

11 

u 

.84375 | 

| 

Vs 1 

.125 

II 

I 

.3125 


% 

.5 

11 

[* i 

.6875 

11 

Vs 

.875 | 


A 

.15625 

11 

n 

.34375 

I 

a? 

.53125 

11 

II 

.71875 

11 

29 
it 2 

.90625 | 


A 1 

.1875 

11 

% 1 

.375 

1 

ft 

.5625 

11 

% 1 

.75 

11 

1 $ 

1 (» 

.9375 | 

1 


[1841 





















































































